The Classical Groups
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The Classical Groups
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Author : Hermann Weyl
language : en
Publisher: Princeton University Press
Release Date : 1946
The Classical Groups written by Hermann Weyl and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1946 with Mathematics categories.
The author discusses symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are important in understanding the group-theoretic structure of quantum mechanics.
Representations And Invariants Of The Classical Groups
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Author : Roe Goodman
language : en
Publisher: Cambridge University Press
Release Date : 2000-01-13
Representations And Invariants Of The Classical Groups written by Roe Goodman 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 2000-01-13 with Mathematics categories.
More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.
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 Subgroup Structure Of The Finite Classical Groups
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Author : Peter B. Kleidman
language : en
Publisher: Cambridge University Press
Release Date : 1990-04-26
The Subgroup Structure Of The Finite Classical Groups written by Peter B. Kleidman 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 1990-04-26 with Mathematics categories.
With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.
The Geometry Of The Classical Groups
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Author : Donald E. Taylor
language : en
Publisher:
Release Date : 1992
The Geometry Of The Classical Groups written by Donald E. Taylor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Groups And Characters
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Author : Larry C. Grove
language : en
Publisher: Wiley-Interscience
Release Date : 1997-06-16
Groups And Characters written by Larry C. Grove and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-16 with Mathematics categories.
Grove combines group theory and ordinary character theory in this challenging, self-contained textbook which include many exercises as well as an entire chapter devoted to important and fully detailed examples.
The Classical Groups
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Author : Hermann Weyl
language : en
Publisher: Princeton University Press
Release Date : 2016-06-02
The Classical Groups written by Hermann Weyl and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-02 with Mathematics categories.
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics. Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful." Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.
The Random Matrix Theory Of The Classical Compact Groups
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Author : Elizabeth S. Meckes
language : en
Publisher: Cambridge University Press
Release Date : 2019-08
The Random Matrix Theory Of The Classical Compact Groups written by Elizabeth S. Meckes 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 2019-08 with Mathematics categories.
Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.
Classical Groups For Physicists
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Author : Brian G Wybourne
language : en
Publisher:
Release Date : 1974
Classical Groups For Physicists written by Brian G Wybourne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Classical Topology And Combinatorial Group Theory
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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-03-25
Classical Topology And Combinatorial Group Theory written by John Stillwell 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 1993-03-25 with Mathematics categories.
This introduction to topology stresses geometric aspects, focusing on historical background and visual interpretation of results. The 2nd edition offers 300 illustrations, numerous exercises, challenging open problems and a new chapter on unsolvable problems.