Combinatorial Methods - Free Groups, Polynomials, and Free Algebras (Hardcover, 2004 ed.)

The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology at the beginning of the 20th Century. This book is divided into three fairly independent parts. Part I provides a brief exposition of several classical techniques in combinatorial group theory, namely, methods of Nielsen, Whitehead, and Tietze. Part II contains the main focus of the book. Here the authors show how the aforementioned techniques of combinatorial group theory found their way into affine algebraic geometry, a fascinating area of mathematics that studies polynomials and polynomial mappings. Part III illustrates how ideas from combinatorial group theory contributed to the theory of free algebras. The focus here is on Schreier varieties of algebras (a variety of algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free in the same variety of algebras).

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	CMS Books in Mathematics
Release date:	November 2003
First published:	2004
Authors:	Vladimir Shpilrain • Alexander Mikhalev • Jie-Tai Yu
Dimensions:	235 x 155 x 21mm (L x W x T)
Format:	Hardcover
Pages:	315
Edition:	2004 ed.
ISBN-13:	978-0-387-40562-9
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Promotions
LSN:	0-387-40562-3
Barcode:	9780387405629

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