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Infinite Dimensional Lie Superalgebras : De Gruyter Expositions in Mathematics - Yuri Bahturin

Infinite Dimensional Lie Superalgebras

De Gruyter Expositions in Mathematics

Hardcover Published: 1st November 1992
ISBN: 9783110129748
Number Of Pages: 260
For Ages: 22+ years old

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The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject.

Editorial Board

Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Katrin Wendland, University of Freiburg, Germany

Honorary Editor

Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia

Titles in planning include

Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)
Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)
Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)
Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)
Ioannis Diamantis, Botjan Gabrovek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

List of Symbols
Basic facts about Lie superalgebras
Some backgroundp. 1
Graded algebrasp. 4
Identical relations of graded algebrasp. 22
The structure of free Lie superalgebras
The free colour Lie superalgebra, s-regular words and monomialsp. 39
Bases of free colour Lie superalgebrasp. 44
The freeness of subalgebras and its corollariesp. 53
Bases and subalgebras of free colour Lie p-superalgebrasp. 69
The lattice of finitely generated subalgebrasp. 75
Free colour Lie super-ringsp. 78
Composition techniques in the theory of Lie superalgebras
The Diamond Lemma for associative ringsp. 81
Universal enveloping algebrasp. 84
The Composition Lemmap. 95
Free products with amalgamated subalgebrap. 105
Identities in enveloping algebras
Main resultsp. 111
Delta-setsp. 123
Identities in enveloping algebras of nilpotent Lie superalgebrasp. 129
The case of characteristic zerop. 136
Irreducible representations of Lie superalgebras
The Jacobson radical of universal enveloping algebrasp. 147
Dimensions of irreducible representationsp. 152
More on restricted enveloping algebrasp. 160
Finiteness conditions for color Lie superalgebras with identities
Various types of finiteness conditions. Examplesp. 175
Maximal condition and Hopf propertyp. 180
Sufficient conditions for residual finitenessp. 201
Representability of Lie superalgebras by matricesp. 210
Bibliographyp. 237
Author Indexp. 247
Subject Indexp. 249
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783110129748
ISBN-10: 3110129744
Series: De Gruyter Expositions in Mathematics
Audience: Professional
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 260
Published: 1st November 1992
Publisher: De Gruyter
Country of Publication: DE
Dimensions (cm): 23.0 x 15.5  x 2.54
Weight (kg): 0.59

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