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This title in other editions

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

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

 

Synopses & Reviews

Publisher Comments:

 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).

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.

Table of Contents

Preface.- Introduction.- I. Groups: Introduction. Classical Techniques. Test Elements. Other Special Elements. Automorphic Orbits.- II. Polynomial Algebras: Introduction. The Jacobian Conjecture. The Cancellation Conjecture. Nagata's Problem. The Embedding Problem. Coordinate Polynomials. Test Polynomials.- III. Free Nielsen-Schreier Algebras: Introduction. Schreier Varieties of Algebras. Rank Theorems and Primitive Elements. Generalized Primitive Elements. Free Leibniz Algebras.- References.- Notations.- Author Index.- Subject Index.

Product Details

ISBN:
9781441923448
Author:
Shpilrain, Vladimir
Publisher:
Springer
Author:
Mikhalev, Alexander
Author:
Yu, Jie-Tai
Location:
New York, NY
Subject:
Geometry - Algebraic
Subject:
Algebraic Geometry
Subject:
Non-associative Rings and Algebras
Subject:
Mathematics-Group Theory
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Algebra
Copyright:
Edition Description:
1st Edition. Softcover version of original hardcover edition 2004
Series:
CMS Books in Mathematics
Publication Date:
20110701
Binding:
TRADE PAPER
Language:
English
Pages:
340
Dimensions:
235 x 155 mm

Related Subjects

Reference » Science Reference » General
Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Group Theory

Combinatorial Methods: Free Groups, Polynomials, and Free Algebras (CMS Books in Mathematics) New Trade Paper
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Product details 340 pages Springer - English 9781441923448 Reviews:
"Synopsis" by , 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.
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