Overview

"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."

Full Product Details

Author:   Vladimir Shpilrain ,  Alexander Mikhalev ,  Jie-tai Yu
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 2004
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   0.504kg
ISBN:  

9781441923448

ISBN 10:   1441923446
Pages:   315
Publication Date:   14 December 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

I Groups.- 1 Classical Techniques of Combinatorial Group Theory.- 2 Test Elements.- 3 Other Special Elements.- 4 Automorphic Orbits.- II Polynomial Algebras.- 5 The Jacobian Conjecture.- 6 The Cancellation Conjecture.- 7 Nagata’s Problem.- 8 The Embedding Problem.- 9 Coordinate Polynomials.- 10 Test Polynomials.- III Free Nielsen-Schreier Algebras.- 11 Schreier Varieties of Algebras.- 12 Rank Theorems and Primitive Elements.- 13 Generalized Primitive Elements.- 14 Free Leibniz Algebras.- References.- Notation Index.- Author Index.

Reviews

From the reviews: This book is devoted to a combinatorial theory of three types of objects: (1) free groups, (2) polynomial algebras and free associative algebras, (3) free algebras of the so-called Nielsen-Schreier varieties of algebras. It considers problems related mainly to the groups of automorphisms of these objects... The authors have done a lot of work to show that the same problems and the same ideas are the moving forces of the three theories. The book contains a good background on the classical results (most of them without proof) and a detailed exposition of the recent results. A large portion of the exposition is devoted to topics in which the authors have made their own contribution. -- MATHEMATICAL REVIEWS The book consists of three parts: groups, polynomial algebras and free Nielsen-Schreier algebras. ! The book contains very interesting material to which the authors have made a valuable contribution. The book includes many open and very important problems. ! The exposition of the material is made with care. So the book could be recommended for students even as a textbook. (Vyacheslav A. Artamonov, Zentralblatt MATH, Vol. 1039 (8), 2004)

"From the reviews: ""This book is devoted to a combinatorial theory of three types of objects: (1) free groups, (2) polynomial algebras and free associative algebras, (3) free algebras of the so-called Nielsen-Schreier varieties of algebras. It considers problems related mainly to the groups of automorphisms of these objects... The authors have done a lot of work to show that the same problems and the same ideas are the moving forces of the three theories. The book contains a good background on the classical results (most of them without proof) and a detailed exposition of the recent results. A large portion of the exposition is devoted to topics in which the authors have made their own contribution."" -- MATHEMATICAL REVIEWS ""The book consists of three parts: groups, polynomial algebras and free Nielsen-Schreier algebras. … The book contains very interesting material to which the authors have made a valuable contribution. The book includes many open and very important problems. … The exposition of the material is made with care. So the book could be recommended for students even as a textbook."" (Vyacheslav A. Artamonov, Zentralblatt MATH, Vol. 1039 (8), 2004)"

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions