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Clifford Algebras and the Classical Groups

1995-10-05 Mathematics
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Release : 1995-10-05
Genre : Mathematics
Kind : eBook
Book Rating : 773/5 ( reviews)

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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. This book was released on 1995-10-05. 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.

Clifford Algebra to Geometric Calculus

1984 Mathematics
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Release : 1984
Genre : Mathematics
Kind : eBook
Book Rating : 615/5 ( reviews)

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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. This book was released on 1984. 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.

Clifford Algebras and their Applications in Mathematical Physics

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 901/5 ( reviews)

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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. This book was released on 2013-03-09. 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

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 440/5 ( reviews)

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Book Synopsis Clifford Algebras by : Rafal Ablamowicz

Download or read book Clifford Algebras written by Rafal Ablamowicz. This book was released on 2012-12-06. 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.

An Introduction to Clifford Algebras and Spinors

2016 Mathematics
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Release : 2016
Genre : Mathematics
Kind : eBook
Book Rating : 926/5 ( reviews)

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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.. This book was released on 2016. 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.

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