Lectures On Exceptional Lie Groups

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Lectures on Exceptional Lie Groups

Author : J. F. Adams
Publisher : University of Chicago Press
ISBN 13 : 9780226005270
Total Pages : 20 pages
Book Rating : 4.0/5 (52 download)

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Book Synopsis Lectures on Exceptional Lie Groups by : J. F. Adams

Download or read book Lectures on Exceptional Lie Groups written by J. F. Adams and published by University of Chicago Press. This book was released on 1996-12 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: J. Frank Adams was internationally known and respected as one of the great algebraic topologists. Adams had long been fascinated with exceptional Lie groups, about which he published several papers, and he gave a series of lectures on the topic. The author's detailed lecture notes have enabled volume editors Zafer Mahmud and Mamoru Mimura to preserve the substance and character of Adams's work. Because Lie groups form a staple of most mathematics graduate students' diets, this work on exceptional Lie groups should appeal to many of them, as well as to researchers of algebraic geometry and topology. J. Frank Adams was Lowndean professor of astronomy and geometry at the University of Cambridge. The University of Chicago Press published his Lectures on Lie Groups and has reprinted his Stable Homotopy and Generalized Homology. Chicago Lectures in Mathematics Series

Lectures on Lie Groups

Author : J. F. Adams
Publisher : University of Chicago Press
ISBN 13 : 0226005305
Total Pages : 192 pages
Book Rating : 4.2/5 (26 download)

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Book Synopsis Lectures on Lie Groups by : J. F. Adams

Download or read book Lectures on Lie Groups written by J. F. Adams and published by University of Chicago Press. This book was released on 1982 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: "[Lectures in Lie Groups] fulfills its aim admirably and should be a useful reference for any mathematician who would like to learn the basic results for compact Lie groups. . . . The book is a well written basic text [and Adams] has done a service to the mathematical community."—Irving Kaplansky

An Introduction to Lie Groups and Lie Algebras

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov

Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Lie Groups

Author : Daniel Bump
Publisher : Springer Science & Business Media
ISBN 13 : 1461480248
Total Pages : 532 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Lie Groups by : Daniel Bump

Download or read book Lie Groups written by Daniel Bump and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.

Lie Groups, Lie Algebras, and Representations

Author : Brian Hall
Publisher : Springer
ISBN 13 : 3319134671
Total Pages : 452 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Lie Groups, Lie Algebras, and Representations by : Brian Hall

Download or read book Lie Groups, Lie Algebras, and Representations written by Brian Hall and published by Springer. This book was released on 2015-05-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette

Notes on Lie Algebras

Author : Hans Samelson
Publisher : Springer Science & Business Media
ISBN 13 : 1461390141
Total Pages : 172 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Notes on Lie Algebras by : Hans Samelson

Download or read book Notes on Lie Algebras written by Hans Samelson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the "exceptional Lie 4 6 7 s algebras" , that just somehow appear in the process). There is also a discus sion of the compact form and other real forms of a (complex) semisimple Lie algebra, and a section on automorphisms. The third chapter brings the theory of the finite dimensional representations of a semisimple Lie alge bra, with the highest or extreme weight as central notion. The proof for the existence of representations is an ad hoc version of the present standard proof, but avoids explicit use of the Poincare-Birkhoff-Witt theorem. Complete reducibility is proved, as usual, with J. H. C. Whitehead's proof (the first proof, by H. Weyl, was analytical-topological and used the exis tence of a compact form of the group in question). Then come H.

Groups and Manifolds

Author : Pietro Giuseppe Fré
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110551209
Total Pages : 496 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Groups and Manifolds by : Pietro Giuseppe Fré

Download or read book Groups and Manifolds written by Pietro Giuseppe Fré and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-12-18 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.

Lie Groups and Algebraic Groups

Author : Arkadij L. Onishchik
Publisher : Springer Science & Business Media
ISBN 13 : 364274334X
Total Pages : 347 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Lie Groups and Algebraic Groups by : Arkadij L. Onishchik

Download or read book Lie Groups and Algebraic Groups written by Arkadij L. Onishchik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.

Lectures on Representation Theory

Author : Jing-Song Huang
Publisher : World Scientific
ISBN 13 : 9789810237257
Total Pages : 206 pages
Book Rating : 4.2/5 (372 download)

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Book Synopsis Lectures on Representation Theory by : Jing-Song Huang

Download or read book Lectures on Representation Theory written by Jing-Song Huang and published by World Scientific. This book was released on 1999 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the lectures given at the Nankai Mathematical Summer School in 1997. It provides an introduction to Lie groups, Lie algebras and their representations as well as introduces some directions of current research for graduate students who have little specialized knowledge in representation theory. It only assumes that the reader has a good knowledge of linear algebra and some basic knowledge of abstract algebra.Parts I-III of the book cover the relatively elementary material of representation theory of finite groups, simple Lie algebras and compact Lie groups. These theories are natural continuation of linear algebra. The last chapter of Part III includes some recent results on extension of Weyl's construction to exceptional groups. Part IV covers some advanced material on infinite-dimensional representations of non-compact groups such as the orbit method, minimal representations and dual pair correspondences, which introduces some directions of the current research in representation theory.

Introduction to Lie Algebras

Author : K. Erdmann
Publisher : Springer Science & Business Media
ISBN 13 : 1846284902
Total Pages : 254 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Introduction to Lie Algebras by : K. Erdmann

Download or read book Introduction to Lie Algebras written by K. Erdmann and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Exceptional Lie Algebras

Author : N. Jacobson
Publisher : CRC Press
ISBN 13 : 9780824713263
Total Pages : 140 pages
Book Rating : 4.7/5 (132 download)

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Book Synopsis Exceptional Lie Algebras by : N. Jacobson

Download or read book Exceptional Lie Algebras written by N. Jacobson and published by CRC Press. This book was released on 1971-06-01 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a set of models for the exceptional Lie algebras over algebraically closed fieldsof characteristic O and over the field of real numbers. The models given are based on the algebras ofCayley numbers (octonions) and on exceptional Jordan algebras. They are also valid forcharacteristics p * 2. The book also provides an introduction to the problem of forms of exceptionalsimple Lie algebras, especially the exceptional D4 's, � 6 's, and � 7 's. These are studied by means ofconcrete realizations of the automorphism groups.Exceptional Lie Algebras is a useful tool for the mathematical public in general-especially thoseinterested in the classification of Lie algebras or groups-and for theoretical physicists.

Lie Algebras and Applications

Author : Francesco Iachello
Publisher : Springer
ISBN 13 : 3540362398
Total Pages : 208 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Lie Algebras and Applications by : Francesco Iachello

Download or read book Lie Algebras and Applications written by Francesco Iachello and published by Springer. This book was released on 2007-02-22 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.

Representation Theory

Author : William Fulton
Publisher : Springer Science & Business Media
ISBN 13 : 9780387974958
Total Pages : 616 pages
Book Rating : 4.9/5 (749 download)

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Book Synopsis Representation Theory by : William Fulton

Download or read book Representation Theory written by William Fulton and published by Springer Science & Business Media. This book was released on 1991 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.

Lie Groups and Lie Algebras - A Physicist's Perspective

Author : Adam M. Bincer
Publisher : Oxford University Press
ISBN 13 : 0199662924
Total Pages : 216 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Lie Groups and Lie Algebras - A Physicist's Perspective by : Adam M. Bincer

Download or read book Lie Groups and Lie Algebras - A Physicist's Perspective written by Adam M. Bincer and published by Oxford University Press. This book was released on 2013 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students in Physics. It starts with a discussion of angular momentum and rotations in terms of the orthogonal group in three dimensions and the unitary group in two dimensions and goes on to deal with these groups in any dimensions. All representations of su(2) are obtained and the Wigner-Eckart theorem is discussed. Casimir operators for the orthogonal and unitary groups are discussed. The exceptional group G2 is introduced as the group of automorphisms of octonions. The symmetric group is used to deal with representations of the unitary groups and the reduction of their Kronecker products. Following the presentation of Cartan's classification of semisimple algebras Dynkin diagrams are described. The book concludes with space-time groups - the Lorentz, Poincare and Liouville groups - and a derivation of the energy levels of the non-relativistic hydrogen atom in n space dimensions.

Quantum Field Theory III: Gauge Theory

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
ISBN 13 : 3642224210
Total Pages : 1141 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Quantum Field Theory III: Gauge Theory by : Eberhard Zeidler

Download or read book Quantum Field Theory III: Gauge Theory written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2011-08-17 with total page 1141 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

Lie Algebras: Theory and Algorithms

Author : W.A. de Graaf
Publisher : Elsevier
ISBN 13 : 0080535453
Total Pages : 407 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Lie Algebras: Theory and Algorithms by : W.A. de Graaf

Download or read book Lie Algebras: Theory and Algorithms written by W.A. de Graaf and published by Elsevier. This book was released on 2000-02-04 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups

Author : Katsuhiko Kuribayashi
Publisher : American Mathematical Soc.
ISBN 13 : 0821838563
Total Pages : 98 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups by : Katsuhiko Kuribayashi

Download or read book Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups written by Katsuhiko Kuribayashi and published by American Mathematical Soc.. This book was released on 2006 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $G$ be a compact, simply connected, simple Lie group. By applying the notion of a twisted tensor product in the senses of Brown as well as of Hess, we construct an economical injective resolution to compute, as an algebra, the cotorsion product which is the $E_2$-term of the cobar type Eilenberg-Moore spectral sequence converging to the cohomology of classifying space of the loop group $LG$. As an application, the cohomology $H^*(BLSpin(10); \mathbb{Z}/2)$ is explicitly determined as an $H^*(BSpin(10); \mathbb{Z}/2)$-module by using effectively the cobar type spectral sequence and the Hochschild spectral sequence, and further, by analyzing the TV-model for $BSpin(10)$.