Hopf algebras

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The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.

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Title Statements

Full title :Hopf algebras / David E. Radford.

Summary

Edition Statements

Publication Date:2012.

Publication Statements

Publisher(s):World Scientific
Place of Publication:Hackensack, N.J
Language:eng
Publication Date:2012.

The Physical Object

Description:1 online resource (xxii, 559 pages).

Edition Identifiers

ISBN:9789814338660, 9814338664, 9789814338660, 1280669403, 9781280669408, 9786613646330, 6613646334
oclc:ocn797852071
LC Classification:QA613.8
Dewey Decimal:512/.55

1. Preliminaries. 1.1. Notation and terminology conventions. 1.2. Rank of a tensor. 1.3. Topological aspects of vector space duals -- 2. Coalgebras. 2.1. Algebras and coalgebras, basic definitions. 2.2. Comatrix identities, the fundamental theorem of coalgebras. 2.3. The dual algebra. 2.4. The wedge product. 2.5. The dual coalgebra. 2.6. Double duals. 2.7. The cofree coalgebra on a vector space -- 3. Representations of coalgebras. 3.1. Rational modules of the dual algebra. 3.2 Comodules. 3.3. M[symbol] and M[symbol]. 3.4. The coradical of a coalgebra. 3.5. Injective comodules. 3.6. Coalgebras which are submodules of their dual algebras. 3.7. Indecomposable coalgebras -- 4. The coradical filtration and related structures. 4.1. Filtrations of coalgebras. 4.2. The wedge product and the coradical filtration. 4.3. Idempotents and the coradical filtration . 4.4. Graded algebras and coalgebras. 4.5. The cofree pointed irreducible coalgebra on a vector space. 4.6. The radical of the dual algebra. 4.7. Free pointed coalgebras associated to coalgebras. 4.8. Linked simple subcoalgebras -- 5. Bialgebras. 5.1. Basic definitions and results. 5.2. The dual bialgebra. 5.3. The free bialgebra on a…