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Author: Alexander Lubotzky
Publisher: American Mathematical Soc.
ISBN: 082182337X
Category : Mathematics
Languages : en
Pages : 134
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Book Description
The n-dimensional representations, over an algebraically closed characteristic zero field k, of a finitely generated group are parameterized by an affine algebraic variety over k. The tangent spaces of this variety are subspaces of spaces of one-cocycles and thus the geometry of the variety is locally related to the cohomology of the group. The cohomology is also related to the prounipotent radical of the proalgebraic hull of the group. This paper exploits these two relations to compute dimensions of representation varieties, especially for nilpotent groups and their generalizations. It also presents the foundations of the theory of representation varieties in an expository, self-contained manner.
Author: Alexander Lubotzky
Publisher: American Mathematical Soc.
ISBN: 082182337X
Category : Mathematics
Languages : en
Pages : 134
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Book Description
The n-dimensional representations, over an algebraically closed characteristic zero field k, of a finitely generated group are parameterized by an affine algebraic variety over k. The tangent spaces of this variety are subspaces of spaces of one-cocycles and thus the geometry of the variety is locally related to the cohomology of the group. The cohomology is also related to the prounipotent radical of the proalgebraic hull of the group. This paper exploits these two relations to compute dimensions of representation varieties, especially for nilpotent groups and their generalizations. It also presents the foundations of the theory of representation varieties in an expository, self-contained manner.
Author: Kyoji Saito
Publisher:
ISBN:
Category : Representations of groups
Languages : en
Pages : 53
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Book Description
Author: Kyoji Saito
Publisher:
ISBN:
Category : Representations of groups
Languages : en
Pages : 15
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Book Description
Author: Gregory W. Brumfiel
Publisher: American Mathematical Soc.
ISBN: 0821804162
Category : Mathematics
Languages : en
Pages : 208
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Book Description
This book is essentially self-contained and requires only a basic abstract algebra course as background. The book includes and extends much of the classical theory of SL(2) representations of groups. Readers will find SL(2) Representations of Finitely Presented Groups relevant to geometric theory of three dimensional manifolds, representations of infinite groups, and invariant theory. Features...... * A new finitely computable invariant H[*p] associated to groups and used to study the SL(2) representations of *p * Invariant theory and knot theory related through SL(2) representations of knot groups.
Author: K. Saito
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Book Description
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
ISBN: 082184377X
Category : Mathematics
Languages : en
Pages : 594
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Book Description
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author: Peter Webb
Publisher: Cambridge University Press
ISBN: 1107162394
Category : Mathematics
Languages : en
Pages : 339
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Book Description
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.
Author: David J. Benson
Publisher: Springer Science & Business Media
ISBN: 3034802609
Category : Mathematics
Languages : en
Pages : 115
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Book Description
The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins’ classification of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas.
Author: C. Musili
Publisher: Springer
ISBN: 9380250851
Category : Mathematics
Languages : en
Pages : 252
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Book Description
Author: Alexander Hahn
Publisher: American Mathematical Soc.
ISBN: 082185089X
Category : Mathematics
Languages : en
Pages : 272
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Book Description
During his lifetime, L. K. Hua played a leading role in and exerted a great influence upon the development in China of modern mathematics, both pure and applied. His mathematical career began in 1931 at Tsinghua University where he continued as a professor for many years. Hua made many significant contributions to number theory, algebra, geometry, complex analysis, numerical analysis, and operations research. In particular, he initiated the study of classical groups in China and developed new matrix methods which, as applied by him as well as his followers, were instrumental in the successful attack of many problems. To honor his memory, a joint China-U.S. conference on Classical Groups and Related Topics was held at Tsinghua University in Beijing in May 1987. This volume represents the proceedings of that conference and contains both survey articles and research papers focusing on classical groups and closely related topics.
