Quantum Groups

A Path to Current Algebra

Ross Street - Collection Australian Mathematical Society Lecture Series

142 pages, parution le 05/04/2007

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Résumé

Algebra has moved well beyond the topics discussed in standard undergraduate texts on "modern algebra". Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn the latest algebraic concepts and techniques.

A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an "algebra". Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a "coalgebra". While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term "quantum group", along with revolutionary new examples, was launched by Drinfel'd in 1986.

Essential for any graduate student or researcher whose research involves quantum groups
Containing the latest algebraic concepts and techniques, this book updates the meaning of "modern algebra"
Includes over 60 worked examples and exercises

L'auteur - Ross Street

Ross Street : Macquarie University, Sydney

Sommaire

Revision of basic structures
Duality between geometry and algebra
The quantum general linear group
Modules and tensor products
Cauchy modules
Algebras
Coalgebras and bialgebras
Dual coalgebras of algebras
Hopf algebras
Representations of quantum groups
Tensor categories
Internal homs and duals
Tensor functors and Yang-Baxter operators
A tortile Yang-Baxter operator for each finite-dimensional vector space
Monoids in tensor categories
Tannaka duality
Adjoining an antipode to a bialgebra
The quantum general linear group again
Solutions to exercises

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Ross Street
Collection	Australian Mathematical Society Lecture Series
Parution	05/04/2007
Nb. de pages	142
Format	15 x 23
Couverture	Broché
Poids	235g
Intérieur	Noir et Blanc
EAN13	9780521695244
ISBN13	978-0-521-69524-4