Enveloping Algebras

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Enveloping Algebras

Author : Jacques Dixmier
Publisher : American Mathematical Soc.
ISBN 13 : 0821805606
Total Pages : 379 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Enveloping Algebras by : Jacques Dixmier

Download or read book Enveloping Algebras written by Jacques Dixmier and published by American Mathematical Soc.. This book was released on 1996 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the graduate student, this is a masterpiece of pedagogical writing, being succinct, wonderfully self-contained and of exceptional precision. --Mathematical Reviews This book, which is the first systematic exposition of the algebraic approach to representations of Lie groups via representations of (or modules over) the corresponding universal enveloping algebras, turned out to be so well written that even today it remains one of the main textbooks and reference books on the subject. In 1992, Jacques Dixmier was awarded the Leroy P. Steele Prize for expository writing in mathematics. The Committee's citation mentioned Enveloping Algebras as one of Dixmier's ``extraordinary books''. Written with unique precision and elegance, the book provides the reader with insight and understanding of this very important subject. For the 1996 printing, Dixmier updated the status of open problems and added some relevant references. The book is suitable as a textbook for a graduate course on enveloping algebras. It is also a valuable reference for graduate students and research mathematicians interested in Lie algebras.

Enveloping Algebras

Author : Diximier
Publisher : Newnes
ISBN 13 : 0444110771
Total Pages : 393 pages
Book Rating : 4.4/5 (441 download)

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Book Synopsis Enveloping Algebras by : Diximier

Download or read book Enveloping Algebras written by Diximier and published by Newnes. This book was released on 2009-02-10 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enveloping Algebras

Lie Superalgebras and Enveloping Algebras

Author : Ian Malcolm Musson
Publisher : American Mathematical Soc.
ISBN 13 : 0821868675
Total Pages : 512 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lie Superalgebras and Enveloping Algebras by : Ian Malcolm Musson

Download or read book Lie Superalgebras and Enveloping Algebras written by Ian Malcolm Musson and published by American Mathematical Soc.. This book was released on 2012-04-04 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on $\mathfrak{g}$. The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the Poincare-Birkhoff-Witt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.

Yang-Baxter Equation and Quantum Enveloping Algebras

Author : Zhongqi Ma
Publisher : World Scientific
ISBN 13 : 9789810213831
Total Pages : 336 pages
Book Rating : 4.2/5 (138 download)

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Book Synopsis Yang-Baxter Equation and Quantum Enveloping Algebras by : Zhongqi Ma

Download or read book Yang-Baxter Equation and Quantum Enveloping Algebras written by Zhongqi Ma and published by World Scientific. This book was released on 1993 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first-ever textbook on the Yang-Baxter equation. A key nonlinear equation for solving two important models in many-body statistical theory - the many-body problem in one dimension with repulsive delta-function interaction presented by Professor Baxter in 1972 - it has become one of the main concerns of physicists and mathematicians in the last ten years. A textbook on this subject which also serves as a reference book is vital for an equation which plays important roles in diverse areas of physics and mathematics like the completely integrable statistical models, conformal field theories, topological field theories, the theory of braid groups, the theory of knots and links, etc. This book arose from lectures given by the author in an attempt to reformulate the results of the rapidly developing research and make the material more accessible. It explains the presentation of the Yang-Baxter equation from statistical models, and expound systematically the meaning and methods of solving for this equation. From the viewpoint of theoretical physics it aims to develop an intuitive understanding of the fundamental knowledge of the Hopf algebras, quantization of Lie bialgebras, and the quantum enveloping algebras, and places emphasis on the introduction of the calculation skill in terms of the physical language.

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

Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras

Author : Shari A. Prevost
Publisher : American Mathematical Soc.
ISBN 13 : 0821825275
Total Pages : 97 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras by : Shari A. Prevost

Download or read book Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras written by Shari A. Prevost and published by American Mathematical Soc.. This book was released on 1992 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold]Z-form of the enveloping algebras for the simply-laced affine Lie algebras to the enveloping algebras associated to the unequal root length affine Lie algebras.

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.

Representation Theory of Algebras

Author : Raymundo Bautista
Publisher : American Mathematical Soc.
ISBN 13 : 9780821803950
Total Pages : 780 pages
Book Rating : 4.8/5 (39 download)

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Book Synopsis Representation Theory of Algebras by : Raymundo Bautista

Download or read book Representation Theory of Algebras written by Raymundo Bautista and published by American Mathematical Soc.. This book was released on 1996 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ICRA VII was held at Cocoyoc, Mexico, in August 1994. This was the second time that the ICRA was held in Mexico: ICRA III took place in Puebla in 1980. The 1994 conference included 62 lectures, all listed in these Proceedings. Not all contributions presented, however, appear in this book. Most papers in this volume are in final form with complete proofs, with the only exception being the paper of Leszczynski and Skowronski, Auslander algebras of tame representation type, that the editors thought useful to include.

Polynomial Identities in Algebras

Author : Onofrio Mario Di Vincenzo
Publisher : Springer Nature
ISBN 13 : 3030631117
Total Pages : 421 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Polynomial Identities in Algebras by : Onofrio Mario Di Vincenzo

Download or read book Polynomial Identities in Algebras written by Onofrio Mario Di Vincenzo and published by Springer Nature. This book was released on 2021-03-22 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. The purpose of the book is to present the current state of the art in the theory of PI-algebras. The review of the classical results in the last few years has pointed out new perspectives for the development of the theory. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems. It is addressed to researchers in the field.

Stably Flat Completions of Universal Enveloping Algebras

Author : A. Yu Pirkovskii
Publisher :
ISBN 13 :
Total Pages : 66 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Stably Flat Completions of Universal Enveloping Algebras by : A. Yu Pirkovskii

Download or read book Stably Flat Completions of Universal Enveloping Algebras written by A. Yu Pirkovskii and published by . This book was released on 2006 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Groups and Lie Algebras I

Author : V.V. Gorbatsevich
Publisher : Springer Science & Business Media
ISBN 13 : 364257999X
Total Pages : 241 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Lie Groups and Lie Algebras I by : V.V. Gorbatsevich

Download or read book Lie Groups and Lie Algebras I written by V.V. Gorbatsevich and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Lie Algebras: Theory and Algorithms

Author : W.A. de Graaf
Publisher : Elsevier
ISBN 13 : 0080535453
Total Pages : 407 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Lie Algebras: Theory and Algorithms by : W.A. de Graaf

Download or read book Lie Algebras: Theory and Algorithms written by W.A. de Graaf and published by Elsevier. This book was released on 2000-02-04 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

Whittaker Modules, Central Characters, and Tensor Products for Quantum Enveloping Algebras

Author : Matthew Ondrus
Publisher :
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Whittaker Modules, Central Characters, and Tensor Products for Quantum Enveloping Algebras by : Matthew Ondrus

Download or read book Whittaker Modules, Central Characters, and Tensor Products for Quantum Enveloping Algebras written by Matthew Ondrus and published by . This book was released on 2004 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinatorial Aspects of Lie Superalgebras

Author : Alexander A. Mikhalev
Publisher : CRC Press
ISBN 13 : 9780849389603
Total Pages : 276 pages
Book Rating : 4.3/5 (896 download)

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Book Synopsis Combinatorial Aspects of Lie Superalgebras by : Alexander A. Mikhalev

Download or read book Combinatorial Aspects of Lie Superalgebras written by Alexander A. Mikhalev and published by CRC Press. This book was released on 1995-06-09 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Aspects of Lie Superalgebras emphasizes the algorithmic and computational aspects of the combinatorial techniques of Lie superalgebras. It is written primarily for mathematicians and scientists who do not have a background in the field of infinite dimensional Lie superalgebras, but who realize the potential uses of the results. Consequently, the discussions provided on the applications of Lie superalgebras theory are clear and comprehensive and, throughout the text, primary attention is given to algorithms and examples. The examples illustrate theoretical results, and the algorithms, which can be used for symbolic calculations with Lie superalgebras, are based on basic and generally applicable rules and theorems. Combinatorial Aspects of Lie Superalgebras contains comprehensive literature citations and provides an excellent reference on the techniques and results of combinatorial theory of Lie superalgebras. Programs that have been developed by the authors for computation are included on a diskette at the back of the book, and complete directions for use are provided.

Hopf Algebras

Author : David E. Radford
Publisher : World Scientific
ISBN 13 : 9814335991
Total Pages : 584 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Hopf Algebras by : David E. Radford

Download or read book Hopf Algebras written by David E. Radford and published by World Scientific. This book was released on 2012 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.

Primeness of Enveloping Algebras

Author : Mark Curtis Wilson
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Primeness of Enveloping Algebras by : Mark Curtis Wilson

Download or read book Primeness of Enveloping Algebras written by Mark Curtis Wilson and published by . This book was released on 1995 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

Author : Vlastimil Dlab
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871454
Total Pages : 508 pages
Book Rating : 4.8/5 (714 download)

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Book Synopsis Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry by : Vlastimil Dlab

Download or read book Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry written by Vlastimil Dlab and published by American Mathematical Soc.. This book was released on with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.