Modular Lie Algebras

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Modular Lie Algebras

Author : Geoge B. Seligman
Publisher : Springer Science & Business Media
ISBN 13 : 3642949851
Total Pages : 175 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Modular Lie Algebras by : Geoge B. Seligman

Download or read book Modular Lie Algebras written by Geoge B. Seligman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the structure of Lie algebras over arbitrary fields is now a little more than thirty years old. The first papers, to my know ledge, which undertook this study as an end in itself were those of JACOBSON (" Rational methods in the theory of Lie algebras ") in the Annals, and of LANDHERR ("Uber einfache Liesche Ringe") in the Hamburg Abhandlungen, both in 1935. Over fields of characteristic zero, these thirty years have seen the ideas and results inherited from LIE, KILLING, E. CARTAN and WEYL developed and given new depth, meaning and elegance by many contributors. Much of this work is presented in [47, 64, 128 and 234] of the bibliography. For those who find the rationalization for the study of Lie algebras in their connections with Lie groups, satisfying counterparts to these connections have been found over general non-modular fields, with the substitution of the formal groups of BOCHNER [40] (see also DIEUDONNE [108]), or that of the algebraic linear groups of CHEVALLEY [71], for the usual Lie group. In particular, the relation with algebraic linear groups has stimulated the study of Lie algebras of linear transformations. When one admits to consideration Lie algebras over a base field of positive characteristic (such are the algebras to which the title of this monograph refers), he encounters a new and initially confusing scene.

Modular Lie Algebras and their Representations

Author : H. Strade
Publisher : CRC Press
ISBN 13 : 1000103390
Total Pages : 318 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Modular Lie Algebras and their Representations by : H. Strade

Download or read book Modular Lie Algebras and their Representations written by H. Strade and published by CRC Press. This book was released on 2020-08-11 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebras, Rings and Modules

Author : Michiel Hazewinkel
Publisher : CRC Press
ISBN 13 : 1482245051
Total Pages : 388 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Algebras, Rings and Modules by : Michiel Hazewinkel

Download or read book Algebras, Rings and Modules written by Michiel Hazewinkel and published by CRC Press. This book was released on 2016-04-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.

Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras

Author : Vyjayanthi Chari
Publisher : American Mathematical Soc.
ISBN 13 : 082180748X
Total Pages : 172 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras by : Vyjayanthi Chari

Download or read book Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras written by Vyjayanthi Chari and published by American Mathematical Soc.. This book was released on 1997 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers dedicated to Richard E. Block, whose research has been largely devoted to the study of Lie algebras of prime characteristic (specifically the classification of simple Lie algebras). The volume presents proceedings of a conference held at the University of California at Riverside in February 1994 on the occasion of his retirement. The conference focused on the interplay between the theory of Lie algebras of prime characteristic, quantum groups, and Lie superalgebras. Titles in this series are co-published with International Press, Cambridge, MA, USA.

Algebraic Groups and Modular Lie Algebras

Author : James E. Humphreys
Publisher : American Mathematical Soc.
ISBN 13 : 0821812718
Total Pages : 80 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Groups and Modular Lie Algebras by : James E. Humphreys

Download or read book Algebraic Groups and Modular Lie Algebras written by James E. Humphreys and published by American Mathematical Soc.. This book was released on 1967 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modular Lie Algebras

Author : George B. Seligman
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Modular Lie Algebras by : George B. Seligman

Download or read book Modular Lie Algebras written by George B. Seligman and published by . This book was released on 1967 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the structure of Lie algebras over arbitrary fields is now a little more than thirty years old. The first papers, to my know ledge, which undertook this study as an end in itself were those of JACOBSON (" Rational methods in the theory of Lie algebras ") in the Annals, and of LANDHERR ("Uber einfache Liesche Ringe") in the Hamburg Abhandlungen, both in 1935. Over fields of characteristic zero, these thirty years have seen the ideas and results inherited from LIE, KILLING, E. CARTAN and WEYL developed and given new depth, meaning and elegance by many contributors. Much of this work is presented in [47, 64, 128 and 234] of the bibliography. For those who find the rationalization for the study of Lie algebras in their connections with Lie groups, satisfying counterparts to these connections have been found over general non-modular fields, with the substitution of the formal groups of BOCHNER [40] (see also DIEUDONNE [108]), or that of the algebraic linear groups of CHEVALLEY [71], for the usual Lie group. In particular, the relation with algebraic linear groups has stimulated the study of Lie algebras of linear transformations. When one admits to consideration Lie algebras over a base field of positive characteristic (such are the algebras to which the title of this monograph refers), he encounters a new and initially confusing scene.

Modular Lie Algebras and their Representations

Author : H. Strade
Publisher : CRC Press
ISBN 13 : 1000146820
Total Pages : 321 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Modular Lie Algebras and their Representations by : H. Strade

Download or read book Modular Lie Algebras and their Representations written by H. Strade and published by CRC Press. This book was released on 2020-08-12 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Lie Algebras

Author : David J Winter
Publisher : Courier Corporation
ISBN 13 : 0486783464
Total Pages : 162 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Abstract Lie Algebras by : David J Winter

Download or read book Abstract Lie Algebras written by David J Winter and published by Courier Corporation. This book was released on 2013-12-01 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Constructions of Lie Algebras and their Modules

Author : George B. Seligman
Publisher : Springer
ISBN 13 : 3540388648
Total Pages : 203 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Constructions of Lie Algebras and their Modules by : George B. Seligman

Download or read book Constructions of Lie Algebras and their Modules written by George B. Seligman and published by Springer. This book was released on 2006-11-14 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Infinite Dimensional Lie Algebras

Author : Victor G. Kac
Publisher : Springer Science & Business Media
ISBN 13 : 1475713827
Total Pages : 267 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Infinite Dimensional Lie Algebras by : Victor G. Kac

Download or read book Infinite Dimensional Lie Algebras written by Victor G. Kac and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Algebras and Related Topics

Author : Daniel J. Britten
Publisher : American Mathematical Soc.
ISBN 13 : 9780821860090
Total Pages : 398 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Lie Algebras and Related Topics by : Daniel J. Britten

Download or read book Lie Algebras and Related Topics written by Daniel J. Britten and published by American Mathematical Soc.. This book was released on 1986 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lie Algebras

Author : Nathan Jacobson
Publisher : Courier Corporation
ISBN 13 : 0486136795
Total Pages : 352 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Lie Algebras by : Nathan Jacobson

Download or read book Lie Algebras written by Nathan Jacobson and published by Courier Corporation. This book was released on 2013-09-16 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Lie Algebras and Their Representations

Author : Seok-Jin Kang
Publisher : American Mathematical Soc.
ISBN 13 : 0821805126
Total Pages : 242 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lie Algebras and Their Representations by : Seok-Jin Kang

Download or read book Lie Algebras and Their Representations written by Seok-Jin Kang and published by American Mathematical Soc.. This book was released on 1996 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.

Introduction to Lie Algebras

Author : K. Erdmann
Publisher : Springer Science & Business Media
ISBN 13 : 1846284902
Total Pages : 251 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Introduction to Lie Algebras by : K. Erdmann

Download or read book Introduction to Lie Algebras written by K. Erdmann and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

An Introduction to Lie Groups and Lie Algebras

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov

Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Lie Groups, Geometry, and Representation Theory

Author : Victor G. Kac
Publisher : Springer
ISBN 13 : 3030021912
Total Pages : 540 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Lie Groups, Geometry, and Representation Theory by : Victor G. Kac

Download or read book Lie Groups, Geometry, and Representation Theory written by Victor G. Kac and published by Springer. This book was released on 2018-12-12 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)

Representations of Semisimple Lie Algebras in the BGG Category O

Author : James E. Humphreys
Publisher : American Mathematical Soc.
ISBN 13 : 1470463261
Total Pages : 289 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Representations of Semisimple Lie Algebras in the BGG Category O by : James E. Humphreys

Download or read book Representations of Semisimple Lie Algebras in the BGG Category O written by James E. Humphreys and published by American Mathematical Soc.. This book was released on 2021-07-14 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook treatment of work leading to the landmark 1979 Kazhdan–Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra g g over C C. The setting is the module category O O introduced by Bernstein–Gelfand–Gelfand, which includes all highest weight modules for g g such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of g g. Basic techniques in category O O such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan–Lusztig Conjecture (due to Beilinson–Bernstein and Brylinski–Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: D D-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category O O, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson–Ginzburg–Soergel.