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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.

Classical Groups and Geometric Algebra

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 192/5 ( reviews)

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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. This book was released on 2002. 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.

Classical Clifford Algebras

2024-04-08 Mathematics
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Release : 2024-04-08
Genre : Mathematics
Kind : eBook
Book Rating : 548/5 ( reviews)

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Book Synopsis Classical Clifford Algebras by : Ilwoo Cho

Download or read book Classical Clifford Algebras written by Ilwoo Cho. This book was released on 2024-04-08. 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

Groups and Characters

2011-09-26 Mathematics
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Release : 2011-09-26
Genre : Mathematics
Kind : eBook
Book Rating : 931/5 ( reviews)

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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. This book was released on 2011-09-26. 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.

The Classical Groups and K-Theory

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 528/5 ( reviews)

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

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