Combinatorial Methods: Free Groups, Polynomials, and Free Algebras (CMS Books in Mathematics) - Softcover

Shpilrain, Vladimir; Mikhalev, Alexander; Yu, Jie-tai

Softcover

ISBN 10: 1441923446 ISBN 13: 9781441923448

Publisher: Springer, 2011

Synopsis

 

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 in the beginning of the 20th Century.

About this title

From the Back Cover

 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 in 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).

Edition details

• Publisher: Springer
• Publication date: 2011
• Language: English
• ISBN 10: 1441923446
• ISBN 13: 9781441923448
• Binding: Paperback
• Number of pages: 327