Combinatorial Aspects of Lie Superalgebras
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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.
Table of Contents
Preliminaries: Lie Superalgebras. Color Lie Superalgebras. Universal Constructions. Group Actions on Free Lie Superalgebras.
Linear Structure: Regular Words. Regular Monomials. Arrangements of Brackets. Bases of Free Color Lie Superalgebras. Dynkin-Specht-Wever Criterion. Equations in Free Lie Superalgebras. Algorithms and Examples.
Free Subalgebras: Weak Algorithm. Reduced Subsets. Main Theorem. Finitely Generated Subalgebras. Subalgebras of Infinite Rank. Algorithms and Examples.
Canonical Bases: Canonical Bases in Associative Algebras. Universal Enveloping Algebras. Canonical Bases in Lie Superalgebras. Free Products. Algorithms and Examples.
Free Differential Calculus: Universal Derivations. Jacobian Matrices. Admissible Elements. The Homogeneous Case. Rank Theorems. Automorphisms and Primitive Elements. Algorithms and Examples.
Appendix - Program Description
Bibliography. Notations. Index.
Each chapter also includes a Comments section, wherein concepts are further discussed and additional sources of information are provided