Varieties Of Representations Of Finitely Generated Groups PDF Download
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Author | : Alexander Lubotzky |
Publisher | : American Mathematical Soc. |
Total Pages | : 134 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 082182337X |
Download Varieties of Representations of Finitely Generated Groups Book in PDF, ePub and Kindle
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 | : |
Total Pages | : 53 |
Release | : 1993 |
Genre | : Representations of groups |
ISBN | : |
Download Representation Varieties of a Finitely Generated Group Into SL2 Or GL2 Book in PDF, ePub and Kindle
Author | : Hirosi Nagao |
Publisher | : Elsevier |
Total Pages | : 443 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483269930 |
Download Representations of Finite Groups Book in PDF, ePub and Kindle
Representations of Finite Groups provides an account of the fundamentals of ordinary and modular representations. This book discusses the fundamental theory of complex representations of finite groups. Organized into five chapters, this book begins with an overview of the basic facts about rings and modules. This text then provides the theory of algebras, including theories of simple algebras, Frobenius algebras, crossed products, and Schur indices with representation-theoretic versions of them. Other chapters include a survey of the fundamental theory of modular representations, with emphasis on Brauer characters. This book discusses as well the module-theoretic representation theory due to Green and includes some topics such as Burry–Carlson's theorem and Scott modules. The final chapter deals with the fundamental results of Brauer on blocks and Fong's theory of covering, and includes some approaches to them. This book is a valuable resource for readers who are interested in the various approaches to the study of the representations of groups.
Author | : Kyoji Saito |
Publisher | : |
Total Pages | : 15 |
Release | : 1994 |
Genre | : Representations of groups |
ISBN | : |
Download Character Variety of Representations of a Finitely Generated Group in SL2 Book in PDF, ePub and Kindle
Author | : Gregory W. Brumfiel |
Publisher | : American Mathematical Soc. |
Total Pages | : 208 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 0821804162 |
Download $SL(2)$ Representations of Finitely Presented Groups Book in PDF, ePub and Kindle
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 | : |
Total Pages | : 12 |
Release | : 1996 |
Genre | : |
ISBN | : |
Download Character Variety of Representations of a Finitely Generated Group in $ SL_2 $ Book in PDF, ePub and Kindle
Author | : Jens Carsten Jantzen |
Publisher | : American Mathematical Soc. |
Total Pages | : 594 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082184377X |
Download Representations of Algebraic Groups Book in PDF, ePub and Kindle
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 |
Total Pages | : 339 |
Release | : 2016-08-19 |
Genre | : Mathematics |
ISBN | : 1107162394 |
Download A Course in Finite Group Representation Theory Book in PDF, ePub and Kindle
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 |
Total Pages | : 115 |
Release | : 2011-11-15 |
Genre | : Mathematics |
ISBN | : 3034802609 |
Download Representations of Finite Groups: Local Cohomology and Support Book in PDF, ePub and Kindle
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 | : Samuel M. Vovsi |
Publisher | : Cambridge University Press |
Total Pages | : 218 |
Release | : 1991-11-28 |
Genre | : Mathematics |
ISBN | : 0521424100 |
Download Topics in Varieties of Group Representations Book in PDF, ePub and Kindle
This book is devoted to the theory of group representations, a young and promising area of modern algebra. It provides a detailed exposition of several central topics in the field, leading to the most current advances and developments. Much of the included material has never been available in book form before. It is intended for a broad audience of researchers and graduate students, working in abstract algebra and its many applications.