Projective Modules Over Lie Algebras Of Cartan Type

Author : Daniel Ken Nakano
Publisher : American Mathematical Soc.
Page : 84 pages
File Size : 41,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825303

Get Book

Projective Modules over Lie Algebras of Cartan Type by Daniel Ken Nakano Pdf

This monograph focuses on extending theorems for the classical Lie algebras in order to determine the structure and representation theory for Lie algebras of Cartan type. More specifically, Nakano investigates the block theory for the restricted universal enveloping algebras of the Lie algebras of Cartan type. The first section employs techniques developed by Holmes and Nakano to prove a Brauer-Humphreys reciprocity law for graded restricted Lie algebras and also to find the decompositions for the intermediate (Verma) modules used in the reciprocity law. The second section uses this information to investigate the structure of projective modules for the Lie algebras of types W and K. The restricted enveloping algebras for these Lie algebras are shown to have one block. Furthermore, Nakano provides a procedure for computing the Cartan invariants for Lie algebras of types W and K, given knowledge about the decomposition of the generalized Verma modules and about the Jantzen matrix of the classical/reductive zero component. Noteworthy for its readability and the continuity of its theme and purpose, this monograph appeals to graduate students and researchers interested in Lie algebras.

Author : Daniel J. Britten,Frank W. Lemire,R. V. Moody
Publisher : American Mathematical Soc.
Page : 398 pages
File Size : 47,7 Mb
Release : 1986
Category : Mathematics
ISBN : 0821860097

Get Book

Lie Algebras and Related Topics by Daniel J. Britten,Frank W. Lemire,R. V. Moody Pdf

As the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.

Author : H. Strade
Publisher : CRC Press
Page : 318 pages
File Size : 49,9 Mb
Release : 2020-08-11
Category : Mathematics
ISBN : 9781000103397

Get Book

Modular Lie Algebras and their Representations by H. Strade Pdf

This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.

Author : George B. Seligman
Publisher : Springer
Page : 203 pages
File Size : 44,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540388647

Get Book

Constructions of Lie Algebras and their Modules by George B. Seligman Pdf

This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.

Author : Georgia Benkart
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 48,9 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821851197

Get Book

Lie Algebras and Related Topics by Georgia Benkart Pdf

The 1984 classification of the finite-dimensional restricted simple Lie algebras over an algebraically closed field of characteristic $p>7$ provided the impetus for a Special Year of Lie Algebras, held at the University of Wisconsin, Madison, during 1987-88. Work done during the Special Year and afterward put researchers much closer toward a solution of the long-standing problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This volume contains the proceedings of a conference on Lie algebras and related topics, held in May 1988 to mark the end of the Special Year. The conference featured lectures on Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras. Many facets of recent research on Lie theory are reflected in the papers presented here, testifying to the richness and diversity of this topic.

Author : Joseph Ferrar,Koichiro Harada
Publisher : Walter de Gruyter
Page : 265 pages
File Size : 43,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110801897

Get Book

The Monster and Lie Algebras by Joseph Ferrar,Koichiro Harada Pdf

Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.

Author : David J Winter
Publisher : Courier Corporation
Page : 162 pages
File Size : 48,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9780486783468

Get Book

Abstract Lie Algebras by David J Winter Pdf

Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology.

Author : Nathan Jacobson
Publisher : Courier Corporation
Page : 352 pages
File Size : 53,8 Mb
Release : 2013-09-16
Category : Mathematics
ISBN : 9780486136790

Get Book

Lie Algebras by Nathan Jacobson Pdf

DIVDefinitive treatment of important subject in modern mathematics. Covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, etc. Index. /div

Author : Marina Avitabile,Jörg Feldvoss,Thomas Weigel
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 46,6 Mb
Release : 2015-11-30
Category : Lie algebras
ISBN : 9781470410230

Get Book

Lie Algebras and Related Topics by Marina Avitabile,Jörg Feldvoss,Thomas Weigel Pdf

This volume contains the proceedings of the Workshop on Lie Algebras, in honor of Helmut Strade's 70th Birthday, held from May 22-24, 2013, at the Università degli Studi di Milano-Bicocca, Milano, Italy. Lie algebras are at the core of several areas of mathematics, such as, Lie groups, algebraic groups, quantum groups, representation theory, homogeneous spaces, integrable systems, and algebraic topology. The first part of this volume combines research papers with survey papers by the invited speakers. The second part consists of several collections of problems on modular Lie algebras, their representations, and the conjugacy of their nilpotent elements as well as the Koszulity of (restricted) Lie algebras and Lie properties of group algebras or restricted universal enveloping algebras.

Author : Zongzhu Lin,Jianpan Wang
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 45,9 Mb
Release : 2009-01-16
Category : Mathematics
ISBN : 9780821845554

Get Book

Representation Theory by Zongzhu Lin,Jianpan Wang Pdf

Nothing provided

Author : George B. Seligman
Publisher : American Mathematical Soc.
Page : 185 pages
File Size : 47,6 Mb
Release : 1981
Category : Mathematics
ISBN : 9780821850084

Get Book

Rational Constructions of Modules for Simple Lie Algebras by George B. Seligman Pdf

This book is directed to researchers in Lie theory and in the theory of linear algebra, associative or otherwise, and to graduate students who have had some background in one or more of these areas.

Author : Santos González
Publisher : Springer Science & Business Media
Page : 429 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401109901

Get Book

Non-Associative Algebra and Its Applications by Santos González Pdf

This volume contains the proceedings of the Third International Conference on Non-Associative Algebra and Its Applications, held in Oviedo, Spain, July 12--17, 1993. The conference brought together specialists from all over the world who work in this interesting and active field, which is currently enjoying much attention. All aspects of non-associative algebra are covered. Topics range from purely mathematical subjects to a wide spectrum of applications, and from state-of-the-art articles to overview papers. This collection will point the way for further research for many years to come. The volume is of interest to researchers in mathematics as well as those whose work involves the application of non-associative algebra in such areas as physics, biology and genetics.

Author : James E. Humphreys
Publisher : Cambridge University Press
Page : 260 pages
File Size : 55,6 Mb
Release : 2006
Category : Mathematics
ISBN : 0521674549

Get Book

Modular Representations of Finite Groups of Lie Type by James E. Humphreys Pdf

A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.

Author : Theodore Gerard Faticoni
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 55,9 Mb
Release : 1993
Category : Mathematics
ISBN : 0821825542

Get Book

Categories of Modules over Endomorphism Rings by Theodore Gerard Faticoni Pdf

It is the goal of the memoir to develop a functorial transfer of properties between [italic capital]A and [script capital]M[subscript italic capital]E, the category of modules over [italic capital]E, that is more sensitive than the traditional starting point, Hom([italic capital]A, ·). This memoir should be accessible to anyone who has a working knowledge of rings, modules, functors, and categories equivalent to that gained by reading Anderson and Fuller's text "Rings and Categories of Modules."

Author : Marly Mandia
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 49,7 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821824238

Get Book

Structures of the Level One Standard Modules for the Affine Lie Algebras $B_l^{(1)}$, $F_4^{(1)}$, and $G_2^{(1)}$ by Marly Mandia Pdf