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.

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.

Clifford Algebra to Geometric Calculus

Author : David Hestenes
Publisher : Springer Science & Business Media
ISBN 13 : 9789027725615
Total Pages : 340 pages
Book Rating : 4.7/5 (256 download)

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Book Synopsis Clifford Algebra to Geometric Calculus by : David Hestenes

Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes and published by Springer Science & Business Media. This book was released on 1984 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.

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 : 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.

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

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.

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 (geometric) Algebras with Applications to Physics, Mathematics, and Engineering

Author : William Eric Baylis
Publisher : Boston : Birkhäuser
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Clifford (geometric) Algebras with Applications to Physics, Mathematics, and Engineering by : William Eric Baylis

Download or read book Clifford (geometric) Algebras with Applications to Physics, Mathematics, and Engineering written by William Eric Baylis and published by Boston : Birkhäuser. This book was released on 1996 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a comprehensive approach to the theoretical, applied and symbolic computational aspects of the subject. Excellent for self-study, leading experts in the field have written on the of topics mentioned above, using an easy approach with efficient geometric language for non-specialists.

The Algebraic Theory of Semigroups, Volume II

Author : Alfred Hoblitzelle Clifford
Publisher : American Mathematical Soc.
ISBN 13 : 0821802720
Total Pages : 370 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Algebraic Theory of Semigroups, Volume II by : Alfred Hoblitzelle Clifford

Download or read book The Algebraic Theory of Semigroups, Volume II written by Alfred Hoblitzelle Clifford and published by American Mathematical Soc.. This book was released on 1961 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multivectors And Clifford Algebra In Electrodynamics

Author : Bernard Jancewicz
Publisher : World Scientific
ISBN 13 : 9814513695
Total Pages : 345 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Multivectors And Clifford Algebra In Electrodynamics by : Bernard Jancewicz

Download or read book Multivectors And Clifford Algebra In Electrodynamics written by Bernard Jancewicz and published by World Scientific. This book was released on 1989-01-01 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clifford algebras are assuming now an increasing role in theoretical physics. Some of them predominantly larger ones are used in elementary particle theory, especially for a unification of the fundamental interactions. The smaller ones are promoted in more classical domains. This book is intended to demonstrate usefulness of Clifford algebras in classical electrodynamics. Written with a pedagogical aim, it begins with an introductory chapter devoted to multivectors and Clifford algebra for the three-dimensional space. In a later chapter modifications are presented necessary for higher dimension and for the pseudoeuclidean metric of the Minkowski space.Among other advantages one is worth mentioning: Due to a bivectorial description of the magnetic field a notion of force surfaces naturally emerges, which reveals an intimate link between the magnetic field and the electric currents as its sources. Because of the elementary level of presentation, this book can be treated as an introductory course to electromagnetic theory. Numerous illustrations are helpful in visualizing the exposition. Furthermore, each chapter ends with a list of problems which amplify or further illustrate the fundamental arguments.

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.

Clifford Algebras and Their Applications in Mathematical Physics

Author : J.S.R. Chisholm
Publisher : Springer Science & Business Media
ISBN 13 : 9400947283
Total Pages : 589 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Clifford Algebras and Their Applications in Mathematical Physics by : J.S.R. Chisholm

Download or read book Clifford Algebras and Their Applications in Mathematical Physics written by J.S.R. Chisholm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Kingdon Clifford published the paper defining his "geometric algebras" in 1878, the year before his death. Clifford algebra is a generalisation to n-dimensional space of quaternions, which Hamilton used to represent scalars and vectors in real three-space: it is also a development of Grassmann's algebra, incorporating in the fundamental relations inner products defined in terms of the metric of the space. It is a strange fact that the Gibbs Heaviside vector techniques came to dominate in scientific and technical literature, while quaternions and Clifford algebras, the true associative algebras of inner-product spaces, were regarded for nearly a century simply as interesting mathematical curiosities. During this period, Pauli, Dirac and Majorana used the algebras which bear their names to describe properties of elementary particles, their spin in particular. It seems likely that none of these eminent mathematical physicists realised that they were using Clifford algebras. A few research workers such as Fueter realised the power of this algebraic scheme, but the subject only began to be appreciated more widely after the publication of Chevalley's book, 'The Algebraic Theory of Spinors' in 1954, and of Marcel Riesz' Maryland Lectures in 1959. Some of the contributors to this volume, Georges Deschamps, Erik Folke Bolinder, Albert Crumeyrolle and David Hestenes were working in this field around that time, and in their turn have persuaded others of the importance of the subject.

Lie Groups

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

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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.

Clifford Algebras and Spinors

Author : Pertti Lounesto
Publisher : Cambridge University Press
ISBN 13 : 0521005515
Total Pages : 352 pages
Book Rating : 4.5/5 (21 download)

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Book Synopsis Clifford Algebras and Spinors by : Pertti Lounesto

Download or read book Clifford Algebras and Spinors written by Pertti Lounesto and published by Cambridge University Press. This book was released on 2001-05-03 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

Author : Alexey P Isaev
Publisher : World Scientific
ISBN 13 : 9811217424
Total Pages : 615 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications by : Alexey P Isaev

Download or read book Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications written by Alexey P Isaev and published by World Scientific. This book was released on 2020-07-16 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.

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.