Quantum groups : a path to current algebra / Ross Street ; technical editor, Ross Moore.

Format:

Book

Author/Creator:

Street, Ross, 1945- author.

Contributor:

Moore, Ross., editor.

Series:

Australian Mathematical Society lecture series ; 19.

Australian Mathematical Society lecture series ; 19

Language:

English

Subjects (All):

Quantum groups.

Algebra.

Physical Description:

1 online resource (xviii, 141 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2007.

Language Note:

English

Summary:

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 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.

Contents:

Cover; Half-title; Series-title; Title; Copyright; Dedication; Contents; Introduction; 1 Revision of basic structures; 2 Duality between geometry and algebra; 3 The quantum general linear group; 4 Modules and tensor products; 5 Cauchy modules; 6 Algebras; 7 Coalgebras and bialgebras; 8 Dual coalgebras of algebras; 9 Hopf algebras; 10 Representations of quantum groups; 11 Tensor categories; 12 Internal homs and duals; 13 Tensor functors and Yang-Baxter operators; 14 A tortile Yang-Baxter operator for each finite-dimensional vector space; 15 Monoids in tensor categories; 16 Tannaka duality

17 Adjoining an antipode to a bialgebra18 The quantum general linear group again; 19 Solutions to Exercises; References; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-15838-9

1-280-75026-X

9786610750269

0-511-26932-3

0-511-26990-0

0-511-26833-5

0-511-32048-5

0-511-61850-6

0-511-26900-5

OCLC:

161997561