The Classical Groups

Download The Classical Groups full books in PDF, epub, and Kindle. Read online The Classical Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

The Classical Groups and K-Theory

Author : Alexander J. Hahn
Publisher : Springer Science & Business Media
ISBN 13 : 3662131528
Total Pages : 589 pages
Book Rating : 4.6/5 (621 download)

DOWNLOAD NOW!

Book Synopsis The Classical Groups and K-Theory by : Alexander J. Hahn

Download or read book The Classical Groups and K-Theory written by Alexander J. Hahn and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups", foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the definition of Lie groups, the analogy between simple classical groups over finite fields and simple classical groups over IR or C had been observed, even if the concept of "simplicity" was not quite the same in both cases. With the discovery of the exceptional simple complex Lie algebras by Killing and E. Cartan, it was natural to look for corresponding groups over finite fields, and already around 1900 this was done by Dickson for the exceptional Lie algebras G and E • However, a deep reason for this 2 6 parallelism was missing, and it is only Chevalley who, in 1955 and 1961, discovered that to each complex simple Lie algebra corresponds, by a uniform process, a group scheme (fj over the ring Z of integers, from which, for any field K, could be derived a group (fj(K).

Groups and Characters

Author : Larry C. Grove
Publisher : John Wiley & Sons
ISBN 13 : 1118030931
Total Pages : 228 pages
Book Rating : 4.1/5 (18 download)

DOWNLOAD NOW!

Book Synopsis Groups and Characters by : Larry C. Grove

Download or read book Groups and Characters written by Larry C. Grove and published by John Wiley & Sons. This book was released on 2011-09-26 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative, full-year course on both group theory and ordinary character theory--essential tools for mathematics and the physical sciences One of the few treatments available combining both group theory and character theory, Groups and Characters is an effective general textbook on these two fundamentally connected subjects. Presuming only a basic knowledge of abstract algebra as in a first-year graduate course, the text opens with a review of background material and then guides readers carefully through several of the most important aspects of groups and characters, concentrating mainly on finite groups. Challenging yet accessible, Groups and Characters features: * An extensive collection of examples surveying many different types of groups, including Sylow subgroups of symmetric groups, affine groups of fields, the Mathieu groups, and symplectic groups * A thorough, easy-to-follow discussion of Polya-Redfield enumeration, with applications to combinatorics * Inclusive explorations of the transfer function and normal complements, induction and restriction of characters, Clifford theory, characters of symmetric and alternating groups, Frobenius groups, and the Schur index * Illuminating accounts of several computational aspects of group theory, such as the Schreier-Sims algorithm, Todd-Coxeter coset enumeration, and algorithms for generating character tables As valuable as Groups and Characters will prove as a textbook for mathematicians, it has broader applications. With chapters suitable for use as independent review units, along with a full bibliography and index, it will be a dependable general reference for chemists, physicists, and crystallographers.

Representations and Invariants of the Classical Groups

Author : Roe Goodman
Publisher : Cambridge University Press
ISBN 13 : 9780521663489
Total Pages : 708 pages
Book Rating : 4.6/5 (634 download)

DOWNLOAD NOW!

Book Synopsis Representations and Invariants of the Classical Groups by : Roe Goodman

Download or read book Representations and Invariants of the Classical Groups written by Roe Goodman and published by Cambridge University Press. This book was released on 2000-01-13 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.

Buildings and Classical Groups

Author : Paul B. Garrett
Publisher : CRC Press
ISBN 13 : 9780412063312
Total Pages : 396 pages
Book Rating : 4.0/5 (633 download)

DOWNLOAD NOW!

Book Synopsis Buildings and Classical Groups by : Paul B. Garrett

Download or read book Buildings and Classical Groups written by Paul B. Garrett and published by CRC Press. This book was released on 1997-04-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Buildings are highly structured, geometric objects, primarily used in the finer study of the groups that act upon them. In Buildings and Classical Groups, the author develops the basic theory of buildings and BN-pairs, with a focus on the results needed to apply it to the representation theory of p-adic groups. In particular, he addresses spherical and affine buildings, and the "spherical building at infinity" attached to an affine building. He also covers in detail many otherwise apocryphal results. Classical matrix groups play a prominent role in this study, not only as vehicles to illustrate general results but as primary objects of interest. The author introduces and completely develops terminology and results relevant to classical groups. He also emphasizes the importance of the reflection, or Coxeter groups and develops from scratch everything about reflection groups needed for this study of buildings. In addressing the more elementary spherical constructions, the background pertaining to classical groups includes basic results about quadratic forms, alternating forms, and hermitian forms on vector spaces, plus a description of parabolic subgroups as stabilizers of flags of subspaces. The text then moves on to a detailed study of the subtler, less commonly treated affine case, where the background concerns p-adic numbers, more general discrete valuation rings, and lattices in vector spaces over ultrametric fields. Buildings and Classical Groups provides essential background material for specialists in several fields, particularly mathematicians interested in automorphic forms, representation theory, p-adic groups, number theory, algebraic groups, and Lie theory. No other available source provides such a complete and detailed treatment.

The Subgroup Structure of the Finite Classical Groups

Author : Peter B. Kleidman
Publisher : Cambridge University Press
ISBN 13 : 052135949X
Total Pages : 317 pages
Book Rating : 4.5/5 (213 download)

DOWNLOAD NOW!

Book Synopsis The Subgroup Structure of the Finite Classical Groups by : Peter B. Kleidman

Download or read book The Subgroup Structure of the Finite Classical Groups written by Peter B. Kleidman and published by Cambridge University Press. This book was released on 1990-04-26 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.

The Spread of Almost Simple Classical Groups

Author : Scott Harper
Publisher : Springer Nature
ISBN 13 : 3030741001
Total Pages : 154 pages
Book Rating : 4.0/5 (37 download)

DOWNLOAD NOW!

Book Synopsis The Spread of Almost Simple Classical Groups by : Scott Harper

Download or read book The Spread of Almost Simple Classical Groups written by Scott Harper and published by Springer Nature. This book was released on 2021-05-25 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies generating sets of almost simple classical groups, by bounding the spread of these groups. Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group, every nontrivial element belongs to a generating pair. Groups with this property are said to be 3/2-generated. Breuer, Guralnick and Kantor conjectured that a finite group is 3/2-generated if and only if every proper quotient is cyclic. We prove a strong version of this conjecture for almost simple classical groups, by bounding the spread of these groups. This involves analysing the automorphisms, fixed point ratios and subgroup structure of almost simple classical groups, so the first half of this monograph is dedicated to these general topics. In particular, we give a general exposition of Shintani descent. This monograph will interest researchers in group generation, but the opening chapters also serve as a general introduction to the almost simple classical groups.

Representations of Finite Classical Groups

Author : A. V. Zelevinsky
Publisher : Springer
ISBN 13 : 3540387110
Total Pages : 189 pages
Book Rating : 4.5/5 (43 download)

DOWNLOAD NOW!

Book Synopsis Representations of Finite Classical Groups by : A. V. Zelevinsky

Download or read book Representations of Finite Classical Groups written by A. V. Zelevinsky and published by Springer. This book was released on 2006-11-14 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Clifford Algebras and the Classical Groups

Author : Ian R. Porteous
Publisher : Cambridge University Press
ISBN 13 : 0521551773
Total Pages : 309 pages
Book Rating : 4.5/5 (215 download)

DOWNLOAD NOW!

Book Synopsis Clifford Algebras and the Classical Groups by : Ian R. Porteous

Download or read book Clifford Algebras and the Classical Groups written by Ian R. Porteous and published by Cambridge University Press. This book was released on 1995-10-05 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G(subscript 2), and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.

The Classical Groups

Author : Hermann Weyl
Publisher :
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.F/5 ( download)

DOWNLOAD NOW!

Book Synopsis The Classical Groups by : Hermann Weyl

Download or read book The Classical Groups written by Hermann Weyl and published by . This book was released on 1946 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics. Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful." Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.

The Random Matrix Theory of the Classical Compact Groups

Author : Elizabeth S. Meckes
Publisher : Cambridge University Press
ISBN 13 : 1108317995
Total Pages : 225 pages
Book Rating : 4.1/5 (83 download)

DOWNLOAD NOW!

Book Synopsis The Random Matrix Theory of the Classical Compact Groups by : Elizabeth S. Meckes

Download or read book The Random Matrix Theory of the Classical Compact Groups written by Elizabeth S. Meckes and published by Cambridge University Press. This book was released on 2019-08-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.

The Geometry of the Classical Groups

Author : Donald E. Taylor
Publisher :
ISBN 13 :
Total Pages : 252 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis The Geometry of the Classical Groups by : Donald E. Taylor

Download or read book The Geometry of the Classical Groups written by Donald E. Taylor and published by . This book was released on 1992 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Structure of Classical Diffeomorphism Groups

Author : Augustin Banyaga
Publisher : Springer Science & Business Media
ISBN 13 : 1475768001
Total Pages : 211 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!

Book Synopsis The Structure of Classical Diffeomorphism Groups by : Augustin Banyaga

Download or read book The Structure of Classical Diffeomorphism Groups written by Augustin Banyaga and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 60's, the work of Anderson, Chernavski, Kirby and Edwards showed that the group of homeomorphisms of a smooth manifold which are isotopic to the identity is a simple group. This led Smale to conjecture that the group Diff'" (M)o of cr diffeomorphisms, r ~ 1, of a smooth manifold M, with compact supports, and isotopic to the identity through compactly supported isotopies, is a simple group as well. In this monograph, we give a fairly detailed proof that DifF(M)o is a simple group. This theorem was proved by Herman in the case M is the torus rn in 1971, as a consequence of the Nash-Moser-Sergeraert implicit function theorem. Thurston showed in 1974 how Herman's result on rn implies the general theorem for any smooth manifold M. The key idea was to vision an isotopy in Diff'"(M) as a foliation on M x [0, 1]. In fact he discovered a deep connection between the local homology of the group of diffeomorphisms and the homology of the Haefliger classifying space for foliations. Thurston's paper [180] contains just a brief sketch of the proof. The details have been worked out by Mather [120], [124], [125], and the author [12]. This circle of ideas that we call the "Thurston tricks" is discussed in chapter 2. It explains how in certain groups of diffeomorphisms, perfectness leads to simplicity. In connection with these ideas, we discuss Epstein's theory [52], which we apply to contact diffeomorphisms in chapter 6.

Classical Groups for Physicists

Author : Brian Garner Wybourne
Publisher :
ISBN 13 : 9780317556346
Total Pages : 415 pages
Book Rating : 4.5/5 (563 download)

DOWNLOAD NOW!

Book Synopsis Classical Groups for Physicists by : Brian Garner Wybourne

Download or read book Classical Groups for Physicists written by Brian Garner Wybourne and published by . This book was released on 1974 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Finite Simple Groups

Author : Robert Wilson
Publisher : Springer Science & Business Media
ISBN 13 : 1848009879
Total Pages : 310 pages
Book Rating : 4.8/5 (48 download)

DOWNLOAD NOW!

Book Synopsis The Finite Simple Groups by : Robert Wilson

Download or read book The Finite Simple Groups written by Robert Wilson and published by Springer Science & Business Media. This book was released on 2009-12-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].

Harmonic Analysis on Classical Groups

Author : Sheng Gong
Publisher : Springer
ISBN 13 : 9783642634987
Total Pages : 265 pages
Book Rating : 4.6/5 (349 download)

DOWNLOAD NOW!

Book Synopsis Harmonic Analysis on Classical Groups by : Sheng Gong

Download or read book Harmonic Analysis on Classical Groups written by Sheng Gong and published by Springer. This book was released on 2012-11-10 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: H.Weyl studied harmonic analysis on compact groups of finite di mension. He proved that an orthonormal system exists and that any continuous function on these groups can be approximated by some tinite linear combination of functions in this system. His research, however, seems to be too abstract to yield an explicit expression for the orthonormal system. Thus, we cannot talk about the form of the approximation, nor about its convergence. iO The simplest example of compact groups is {e }, on which there exists an orthonormal system inO { e }, n = 0, ± 1, ± 2 , ... , namely 1 J2" ." ." {I, for n = m; - e,n"e-1m"dO = 2n 0 0, for n =;6 m. The harmonic analysis on this compact group refers to the whole Fourier analysis. So far, extensive literature has been available on this topic. Its remarkable progress is evidenced by the great monograph of seven-hundred pages in two volumes written by A. Zygmund in 1959. iO An immediate extension for {e } is group U", which consists of all n X n square matrices U satisfying ufj' = I, where fj' denotes the conjugate transpose matrix of U. As for construction, there is a close relation between the group U and the group S03. Besides, 2 the application of U" has been found more and more important in physics.

Theory of Finite Simple Groups

Author : Gerhard Michler
Publisher : Cambridge University Press
ISBN 13 : 0521866251
Total Pages : 638 pages
Book Rating : 4.5/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Theory of Finite Simple Groups by : Gerhard Michler

Download or read book Theory of Finite Simple Groups written by Gerhard Michler and published by Cambridge University Press. This book was released on 2006-09-21 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first representation theoretic and algorithmic approach to the theory of abstract finite simple groups.

Lie Groups

Author : Claudio Procesi
Publisher : Springer Science & Business Media
ISBN 13 : 0387289291
Total Pages : 616 pages
Book Rating : 4.3/5 (872 download)

DOWNLOAD NOW!

Book Synopsis Lie Groups by : Claudio Procesi

Download or read book Lie Groups written by Claudio Procesi and published by Springer Science & Business Media. This book was released on 2007-10-17 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. In Lie Groups: An Approach through Invariants and Representations, the author's masterful approach gives the reader a comprehensive treatment of the classical Lie groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis. By covering sufficient background material, the book is made accessible to a reader with a relatively modest mathematical background. Historical information, examples, exercises are all woven into the text. This unique exposition is suitable for a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and mathematical physics.