Clifford Algebras And The Classical Groups

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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)

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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.

Classical Groups and Geometric Algebra

Author : Larry C. Grove
Publisher : American Mathematical Soc.
ISBN 13 : 0821820192
Total Pages : 181 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Classical Groups and Geometric Algebra by : Larry C. Grove

Download or read book Classical Groups and Geometric Algebra written by Larry C. Grove and published by American Mathematical Soc.. This book was released on 2002 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level text on the classical groups: groups of matrices, or (more often) quotients of matrix groups by small normal subgroups. It pulls together into a single source the basic facts about classical groups defined over fields, together with the required geometrical background information, from first principles. The chief prerequisites are basic linear algebra and abstract algebra, including fundamentals of group theory and some Galois Theory. The author teaches at the U. of Arizona. c. Book News Inc.

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)

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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.

Classical Clifford Algebras

Author : Ilwoo Cho
Publisher : CRC Press
ISBN 13 : 1040001548
Total Pages : 135 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Classical Clifford Algebras by : Ilwoo Cho

Download or read book Classical Clifford Algebras written by Ilwoo Cho and published by CRC Press. This book was released on 2024-04-08 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical Clifford Algebras: Operator-Algebraic and Free-Probabilistic Approaches offers novel insights through operator-algebraic and free-probabilistic models. By employing these innovative methods, the author sheds new light on the intrinsic connections between Clifford algebras and various mathematical domains. This monograph should be an essential addition to the library of any researchers interested in Clifford Algebras or Algebraic Geometry more widely. Features Includes multiple examples and applications Suitable for postgraduates and researchers working in Algebraic Geometry Takes an innovative approach to a well-established topic

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)

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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).

Clifford Algebras

Author : Rafal Ablamowicz
Publisher : Springer Science & Business Media
ISBN 13 : 1461220440
Total Pages : 635 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Clifford Algebras by : Rafal Ablamowicz

Download or read book Clifford Algebras written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.

Quaternions, Clifford Algebras and Relativistic Physics

Author : Patrick R. Girard
Publisher : Springer Science & Business Media
ISBN 13 : 3764377917
Total Pages : 177 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Quaternions, Clifford Algebras and Relativistic Physics by : Patrick R. Girard

Download or read book Quaternions, Clifford Algebras and Relativistic Physics written by Patrick R. Girard and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism, and general relativity.

Clifford Algebras: An Introduction

Author : D. J. H. Garling
Publisher : Cambridge University Press
ISBN 13 : 9781107422193
Total Pages : 210 pages
Book Rating : 4.4/5 (221 download)

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Book Synopsis Clifford Algebras: An Introduction by : D. J. H. Garling

Download or read book Clifford Algebras: An Introduction written by D. J. H. Garling and published by Cambridge University Press. This book was released on 2011-06-23 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah-Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell's equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background - including multilinear algebra, quadratic spaces and finite-dimensional real algebras - easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts.

An Introduction to Clifford Algebras and Spinors

Author : Jayme Vaz Jr.
Publisher : Oxford University Press
ISBN 13 : 0198782926
Total Pages : 257 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis An Introduction to Clifford Algebras and Spinors by : Jayme Vaz Jr.

Download or read book An Introduction to Clifford Algebras and Spinors written by Jayme Vaz Jr. and published by Oxford University Press. This book was released on 2016 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.

Clifford Algebras: An Introduction

Author : D. J. H. Garling
Publisher : Cambridge University Press
ISBN 13 : 1107096383
Total Pages : 209 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Clifford Algebras: An Introduction by : D. J. H. Garling

Download or read book Clifford Algebras: An Introduction written by D. J. H. Garling and published by Cambridge University Press. This book was released on 2011-06-23 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.

Clifford Algebras in Analysis and Related Topics

Author : John Ryan
Publisher : CRC Press
ISBN 13 : 1351460277
Total Pages : 384 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Clifford Algebras in Analysis and Related Topics by : John Ryan

Download or read book Clifford Algebras in Analysis and Related Topics written by John Ryan and published by CRC Press. This book was released on 2018-03-09 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.

Clifford Algebras and their Applications in Mathematical Physics

Author : A. Micali
Publisher : Springer Science & Business Media
ISBN 13 : 9401580901
Total Pages : 509 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Clifford Algebras and their Applications in Mathematical Physics by : A. Micali

Download or read book Clifford Algebras and their Applications in Mathematical Physics written by A. Micali and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers presented at the Second Workshop on Clifford Algebras and their Applications in Mathematical Physics. These papers range from various algebraic and analytic aspects of Clifford algebras to applications in, for example, gauge fields, relativity theory, supersymmetry and supergravity, and condensed phase physics. Included is a biography and list of publications of Mário Schenberg, who, next to Marcel Riesz, has made valuable contributions to these topics. This volume will be of interest to mathematicians working in the fields of algebra, geometry or special functions, to physicists working on quantum mechanics or supersymmetry, and to historians of mathematical physics.

Clifford Algebras

Author : Daniel Klawitter
Publisher : Springer
ISBN 13 : 3658076186
Total Pages : 228 pages
Book Rating : 4.6/5 (58 download)

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Book Synopsis Clifford Algebras by : Daniel Klawitter

Download or read book Clifford Algebras written by Daniel Klawitter and published by Springer. This book was released on 2014-10-29 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are examined. The author applies this theory and the developed methods to the homogeneous Clifford algebra model corresponding to Euclidean geometry. Moreover, kinematic mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework.

Clifford Algebras and their Applications in Mathematical Physics

Author : Rafał Abłamowicz
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641825
Total Pages : 500 pages
Book Rating : 4.6/5 (418 download)

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Book Synopsis Clifford Algebras and their Applications in Mathematical Physics by : Rafał Abłamowicz

Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafał Abłamowicz and published by Springer Science & Business Media. This book was released on 2000 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.

Clifford Algebras and Dirac Operators in Harmonic Analysis

Author : John E. Gilbert
Publisher : Cambridge University Press
ISBN 13 : 9780521346542
Total Pages : 346 pages
Book Rating : 4.3/5 (465 download)

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Book Synopsis Clifford Algebras and Dirac Operators in Harmonic Analysis by : John E. Gilbert

Download or read book Clifford Algebras and Dirac Operators in Harmonic Analysis written by John E. Gilbert and published by Cambridge University Press. This book was released on 1991-07-26 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to unite the seemingly disparate topics of Clifford algebras, analysis on manifolds, and harmonic analysis. The authors show how algebra, geometry, and differential equations play a more fundamental role in Euclidean Fourier analysis. They then link their presentation of the Euclidean theory naturally to the representation theory of semi-simple Lie groups.

Geometric Differentiation

Author : I. R. Porteous
Publisher : Cambridge University Press
ISBN 13 : 9780521002646
Total Pages : 354 pages
Book Rating : 4.0/5 (26 download)

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Book Synopsis Geometric Differentiation by : I. R. Porteous

Download or read book Geometric Differentiation written by I. R. Porteous and published by Cambridge University Press. This book was released on 2001-12-13 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a revised version of the popular Geometric Differentiation, first edition.

Quadratic Mappings and Clifford Algebras

Author : Jacques Helmstetter
Publisher : Springer Science & Business Media
ISBN 13 : 3764386061
Total Pages : 512 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Quadratic Mappings and Clifford Algebras by : Jacques Helmstetter

Download or read book Quadratic Mappings and Clifford Algebras written by Jacques Helmstetter and published by Springer Science & Business Media. This book was released on 2008-05-24 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods.