Umfang:
Online-Ressource (XII, 315 p, online resource)
ISBN:
9780387217246
Serie:
CMS Books in Mathematics, Ouvrages de mathématiques de la SMC
Inhalt:
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)
Weitere Ausg.:
ISBN 9781441923448
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Michalev, Aleksandr A., 1965 - Combinatorial methods New York : Springer, 2004 ISBN 0387405623
Weitere Ausg.:
ISBN 9781441923448
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Kombinatorische Gruppentheorie
;
Lie-Algebra
;
Algebraische Geometrie
;
Affine Geometrie
DOI:
10.1007/978-0-387-21724-6
URL:
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