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Book: Combinatorial Methods: Free groups, Polynomials, and Free Algebras

TitleCombinatorial Methods: Free groups, Polynomials, and Free Algebras
Authors
Issue Date2003
PublisherSpringer-Verlag.
Citation
Shpilrain, V, Mikhalev, AA and Yu, J. Combinatorial Methods: Free groups, Polynomials, and Free Algebras. New York: Springer-Verlag, 2003 How to Cite?
AbstractThe 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).
Persistent Identifierhttp://hdl.handle.net/10722/119230
ISBN
ISSN
Series/Report no.CMS Books in Mathematics

 

DC FieldValueLanguage
dc.contributor.authorShpilrain, Ven_HK
dc.contributor.authorMikhalev, AAen_HK
dc.contributor.authorYu, Jen_HK
dc.date.accessioned2010-09-26T08:41:58Z-
dc.date.available2010-09-26T08:41:58Z-
dc.date.issued2003en_HK
dc.identifier.citationShpilrain, V, Mikhalev, AA and Yu, J. Combinatorial Methods: Free groups, Polynomials, and Free Algebras. New York: Springer-Verlag, 2003-
dc.identifier.isbn978-0-387-40562-9-
dc.identifier.issn1613-5237-
dc.identifier.urihttp://hdl.handle.net/10722/119230-
dc.description.abstractThe 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).-
dc.languageengen_HK
dc.publisherSpringer-Verlag.en_HK
dc.relation.ispartofseriesCMS Books in Mathematics-
dc.titleCombinatorial Methods: Free groups, Polynomials, and Free Algebrasen_HK
dc.typeBooken_HK
dc.identifier.emailYu, J: yujt@hkusua.hku.hken_HK
dc.identifier.emailShpilrain, V: shpil@submaths.hku.hken_HK
dc.identifier.emailMikhalev, AA: sasha@submaths.hku.hken_HK
dc.identifier.authorityYu, J=rp00834en_HK
dc.identifier.doi10.1007/978-0-387-21724-6-
dc.identifier.hkuros85609en_HK
dc.identifier.spage312en_HK

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