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Mathematics - Algebra | Algebra VI - Combinatorial and Asymptotic Methods of Algebra. Non-Associative Structures

Algebra VI

Combinatorial and Asymptotic Methods of Algebra. Non-Associative Structures

Series: Encyclopaedia of Mathematical Sciences, Vol. 57

Volume package: Algebra

Kostrikin, A.I., Shafarevich, I.R. (Eds.)

Translated by Dimitric, R.

Original Russian edition published by VINITI, Moscow, 1990

1995, VII, 290 p.

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  • About this book

This book contains two contributions: "Combinatorial and Asymptotic Methods in Algebra" by V.A. Ufnarovskij is a survey of various combinatorial methods in infinite-dimensional algebras, widely interpreted to contain homological algebra and vigorously developing computer algebra, and narrowly interpreted as the study of algebraic objects defined by generators and their relations. The author shows how objects like words, graphs and automata provide valuable information in asymptotic studies. The main methods emply the notions of Gröbner bases, generating functions, growth and those of homological algebra. Treated are also problems of relationships between different series, such as Hilbert, Poincare and Poincare-Betti series. Hyperbolic and quantum groups are also discussed. The reader does not need much of background material for he can find definitions and simple properties of the defined notions introduced along the way. "Non-Associative Structures" by E.N.Kuz'min and I.P.Shestakov surveys the modern state of the theory of non-associative structures that are nearly associative. Jordan, alternative, Malcev, and quasigroup algebras are discussed as well as applications of these structures in various areas of mathematics and primarily their relationship with the associative algebras. Quasigroups and loops are treated too. The survey is self-contained and complete with references to proofs in the literature. The book will be of great interest to graduate students and researchers in mathematics, computer science and theoretical physics.

Content Level » Research

Keywords » Combinatorial algebra - Malcev Algebren - Wachstum - asymptotic methods - asymptotische Methoden - growth - kombinatorische Algebra - malcev algebras - nicht-assoziative Algebren - non-associative algebras

Related subjects » Algebra - Geometry & Topology - Theoretical, Mathematical & Computational Physics

Table of contents 

I. Combinatorial and Asymptotic Methods in Algebra.- II. Non-Associative Structures.- Author Index.

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