Combinatorial Methods : Free Groups, Polynomials, and Free Algebras
Language: English
Published by Springer, 2011
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Druck auf Anfrage Neuware - Printed after ordering - This book is about three seemingly independent areas of mathematics: combinatorial group theory, the theory of Lie algebras and affine algebraic geometry. Indeed, for many years these areas were being developed fairly independently. Combinatorial group theory, the oldest of the three, was born in the beginning of the 20th century as a branch of low-dimensional topology. Very soon, it became an important area of mathematics with its own powerful techniques. In the 1950s, combinatorial group theory started to influence, rather substantially, the theory of Lie algebrasj thus combinatorial theory of Lie algebras was shaped, although the origins of the theory can be traced back to the 1930s. In the 1960s, B. Buchberger introduced what is now known as Gröbner bases. This marked the beginning of a new, 'combinatorial', era in commu tative algebra. It is not very likely that Buchberger was directly influenced by ideas from combinatorial group theory, but his famous algorithm bears resemblance to Nielsen's method, although in a more sophisticated form.…
Seller Inventory # 9781441923448
- Title
- Combinatorial Methods : Free Groups, Polynomials, and Free Algebras
- Author
- Vladimir Shpilrain
- Publisher
- Springer
- Publication year
- 2011
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 1441923446
- ISBN 13
- 9781441923448
- Item weight
- 499 grams
- Dimensions
- 235x155x18 mm
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.
"Synopsis" may belong to another edition of 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).
"About the title" may belong to another edition of this title.
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