Clifford Algebras And Orthogonal Groups

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Clifford Algebras And Orthogonal Groups

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Author : Michael Philip Froman
language : en
Publisher:
Release Date : 1968

Clifford Algebras And Orthogonal Groups written by Michael Philip Froman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.

Clifford Algebras And Spin Representations Of Orthogonal Groups

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Author : Janice Elizabeth Griffiths
language : en
Publisher:
Release Date : 1976

Clifford Algebras And Spin Representations Of Orthogonal Groups written by Janice Elizabeth Griffiths and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.

Spinors Clifford And Cayley Algebras

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Author : Robert Hermann
language : en
Publisher: Math-Sci Press
Release Date : 1974

Spinors Clifford And Cayley Algebras written by Robert Hermann and has been published by Math-Sci Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.

Orthogonal And Symplectic Clifford Algebras

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Author : A. Crumeyrolle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Orthogonal And Symplectic Clifford Algebras written by A. Crumeyrolle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.

Clifford Algebras And The Classical Groups

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Author : Ian R. Porteous
language : en
Publisher: Cambridge University Press
Release Date : 1995-10-05

Clifford Algebras And The Classical Groups written by Ian R. Porteous and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-05 with Mathematics categories.

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 Algebraic Theory Of Spinors And Clifford Algebras

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Author : Claude Chevalley
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-12-13

The Algebraic Theory Of Spinors And Clifford Algebras written by Claude Chevalley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-13 with Mathematics categories.

In 1982, Claude Chevalley expressed three specific wishes with respect to the publication of his Works. First, he stated very clearly that such a publication should include his non technical papers. His reasons for that were two-fold. One reason was his life long commitment to epistemology and to politics, which made him strongly opposed to the view otherwise currently held that mathematics involves only half of a man. As he wrote to G. C. Rota on November 29th, 1982: "An important number of papers published by me are not of a mathematical nature. Some have epistemological features which might explain their presence in an edition of collected papers of a mathematician, but quite a number of them are concerned with theoretical politics ( . . . ) they reflect an aspect of myself the omission of which would, I think, give a wrong idea of my lines of thinking". On the other hand, Chevalley thought that the Collected Works of a mathematician ought to be read not only by other mathematicians, but also by historians of science.

Clifford Algebras And Lie Theory

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Author : Eckhard Meinrenken
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-28

Clifford Algebras And Lie Theory written by Eckhard Meinrenken and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-28 with Mathematics categories.

This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.

Clifford Algebras And Zeons Geometry To Combinatorics And Beyond

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Author : George Stacey Staples
language : en
Publisher: World Scientific
Release Date : 2019-09-24

Clifford Algebras And Zeons Geometry To Combinatorics And Beyond written by George Stacey Staples and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-24 with Mathematics categories.

Clifford algebras have many well-known applications in physics, engineering, and computer graphics. Zeon algebras are subalgebras of Clifford algebras whose combinatorial properties lend them to graph-theoretic applications such as enumerating minimal cost paths in dynamic networks. This book provides a foundational working knowledge of zeon algebras, their properties, and their potential applications in an increasingly technological world.As a graduate-level or advanced undergraduate-level mathematics textbook, it is suitable for self-study by researchers interested in new approaches to existing combinatorial problems and applications (wireless networks, Boolean satisfiability, coding theory, etc.).As the first textbook to explore algebraic and combinatorial properties of zeon algebras in depth, it is suitable for interdisciplinary study in analysis, algebra, and combinatorics. The material is complemented by the CliffMath software package for Mathematica, which is freely available through the book's webpage.

Classical Groups And Geometric Algebra

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Author : Larry C. Grove
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Classical Groups And Geometric Algebra written by Larry C. Grove and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

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.

Quaternions Clifford Algebras And Relativistic Physics

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Author : Patrick R. Girard
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25

Quaternions Clifford Algebras And Relativistic Physics written by Patrick R. Girard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-25 with Mathematics categories.

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.