Lectures On Linear Groups

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Lectures On Linear Groups

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Author : Onorato Timothy O'Meara
language : en
Publisher: American Mathematical Soc.
Release Date : 1974

Lectures On Linear Groups written by Onorato Timothy O'Meara 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 1974 with Mathematics categories.

Lectures On Linear Groups

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Author : O. T. O'Meara
language : en
Publisher:
Release Date : 1977

Lectures On Linear Groups written by O. T. O'Meara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.

Lectures On Lie Groups And Lie Algebras

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Author : Roger William Carter
language : en
Publisher:
Release Date : 1995

Lectures On Lie Groups And Lie Algebras written by Roger William Carter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

In this excellent introduction to the theory of Lie groups and Lie algebras, three of the leading figures in this area have written up their lectures from an LMS/SERC sponsored short course in 1993. Together these lectures provide an elementary account of the theory that is unsurpassed. In the first part Roger Carter concentrates on Lie algebras and root systems. In the second Graeme Segal discusses Lie groups. And in the final part, Ian Macdonald gives an introduction to special linear groups. Anybody requiring an introduction to the theory of Lie groups and their applications should look no further than this book.

Lectures On Linear Groups

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Author : O. T. O'Meara
language : en
Publisher:
Release Date : 1974

Lectures On Linear Groups written by O. T. O'Meara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Automorphisms categories.

The notes in this volume evolved from lectures at the California Institute of Technology during the spring of 1968, from ten survey lectures on classical and Chevalley groups at an NSF Regional Conference at Arizona State University in March 1973, and from lectures on linear groups at the University of Notre Dame in the fall of 1973. The author's goal in these expository lectures was to explain the isomorphism theory of linear groups over integral domains as illustrated by the theorem \mathrm{PSL}_n({\mathfrak o})\cong\mathrm{PSL}_{n_1}({\mathfrak o}_1)\Longleftrightarrow n=n_1\quad\mathrm{and.

Lectures On Lie Groups

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Author : Wu Yi Hsiang
language : en
Publisher: World Scientific
Release Date : 2000

Lectures On Lie Groups written by Wu Yi Hsiang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

This invaluable book provides a concise and systematic introduction to the theory of compact connected Lie groups and their representations, as well as a complete presentation of the structure and classification theory. It uses a non-traditional approach and organization. There is a proper balance between, and a natural combination of, the algebraic and geometric aspects of Lie theory, not only in technical proofs but also in conceptual viewpoints. For example, the orbital geometry of adjoint action, is regarded as the geometric organization of the totality of non-commutativity of a given compact connected Lie group, while the maximal tori theorem of . Cartan and the Weyl reduction of the adjoint action on G to the Weyl group action on a chosen maximal torus are presented as the key results that provide a clear-cut understanding of the orbital geometry.

Algebraic Groups

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Author : J. S. Milne
language : en
Publisher: Cambridge University Press
Release Date : 2017-09-21

Algebraic Groups written by J. S. Milne 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 2017-09-21 with Mathematics categories.

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

A Course In Finite Group Representation Theory

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Author : Peter Webb
language : en
Publisher: Cambridge University Press
Release Date : 2016-08-19

A Course In Finite Group Representation Theory written by Peter Webb 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 2016-08-19 with Mathematics categories.

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Lectures On Lie Groups Second Edition

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Author : Wu-yi Hsiang
language : en
Publisher: World Scientific
Release Date : 2017-04-07

Lectures On Lie Groups Second Edition written by Wu-yi Hsiang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-07 with Mathematics categories.

This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive 'tour of revisiting' the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartan's theory on Lie groups and symmetric spaces.With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books.We begin our revisiting with the compact theory which is much simpler than that of the general semi-simple Lie theory; mainly due to the well fittings between the Frobenius-Schur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 1-4). It is a wonderful reality of the Lie theory that the clear-cut orbital geometry of the adjoint action of compact Lie groups on themselves (i.e. the geometry of conjugacy classes) is not only the key to understand the compact theory, but it actually already constitutes the central core of the entire semi-simple theory, as well as that of the symmetric spaces (cf. Lectures 5-9). This is the main reason that makes the succeeding generalizations to the semi-simple Lie theory, and then further to the Cartan theory on Lie groups and symmetric spaces, conceptually quite natural, and technically rather straightforward.

Seminar On Algebraic Groups And Related Finite Groups

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Author : Armand Borel
language : en
Publisher:
Release Date : 1970

Seminar On Algebraic Groups And Related Finite Groups written by Armand Borel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.

Character Theory Of Finite Groups

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Author : I. Martin Isaacs
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-11-21

Character Theory Of Finite Groups written by I. Martin Isaacs 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 2006-11-21 with Mathematics categories.

Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group. The book begins by developing the module theory of complex group algebras. After the module-theoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging. In addition to the development of the basic theory (using a cleaner notation than previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters. This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory, appearing in the bibliography of almost every research paper in the subject. It is largely self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.