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[null,"1.","Record Nr.",null,"UNINA9910809651203321"]
[null,null,"Autore",null,"Radford David E"]
[null,null,"Titolo",null,"Hopf algebras / / David E. Radford"]
[null,null,"Pubbl/distr/stampa",null,"Hackensack, N.J., : World Scientific, 2012"]
[null,null,"ISBN",null,"1-280-66940-3"]
[{"$nulls":4},"9786613646330"]
[{"$nulls":4},"981-4338-66-4"]
[null,null,"Edizione",null,"[1st ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource"]
[null,null,"Collana",null,"Series on knots and everything ; ; v. 49"]
[null,null,"Classificazione",null,"MAT 160f"]
[{"$nulls":4},"SK 230"]
[null,null,"Disciplina",null,"512/.55"]
[null,null,"Soggetti",null,"Hopf algebras"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[{"$nulls":3},"Livello bibliografico","Monografia"]
[{"$nulls":3},"Note generali","Description based upon print version of record."]
[{"$nulls":3},"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Intro -- Contents -- Preface -- 1. Preliminaries -- 1.1 Notation and terminology conventions -- 1.2 Rank of a tensor -- 1.3 Topological aspects of vector space duals -- Chapter notes -- 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 -- Chapter notes -- 3. Representations of coalgebras -- 3.1 Rational modules of the dual algebra -- 3.2 Comodules -- 3.3 Mr and Mr -- 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 -- Chapter notes -- 4. The coradical .ltration 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 -- Chapter notes -- 5. Bialgebras -- 5.1 Basic definitions and results -- 5.2 The dual bialgebra -- 5.3 The free bialgebra on a coalgebra and related constructions -- 5.4 The universal enveloping algebra -- 5.5 The cofree bialgebra on an algebra -- 5.6 Filtrations and gradings of bialgebras -- 5.7 Representations of bialgebras -- Chapter notes -- 6. The convolution algebra -- 6.1 Definition and basic properties -- 6.2 Invertible elements in the "]
[{"$nulls":4},"convolution algebra -- Chapter notes -- 7. Hopf algebras -- 7.1 Definition of Hopf algebra, the antipode -- 7.2 Q-binomial symbols -- 7.3 Two families of examples -- 7.4 The dual Hopf algebra -- 7.5 The free Hopf algebra on a coalgebra."]
[{"$nulls":4},"7.6 When a bialgebra is a Hopf algebra -- 7.7 Two-cocycles, pairings, and skew pairings of bialgebras -- 7.8 Twists of bialgebras -- 7.9 Filtrations and gradings on Hopf algebras -- 7.10 The cofree pointed irreducible Hopf algebra on an algebra -- 7.11 The shuffle algebra -- Chapter notes -- 8. Hopf modules and co-Hopf modules -- 8.1 Definition of Hopf module and examples -- 8.2 The structure of Hopf modules -- 8.3 Co-Hopf modules -- 8.4 A basic co-Hopf module and its dual -- Chapter notes -- 9. Hopf algebras as modules over Hopf subalgebras -- 9.1 Filtrations whose base term is a Hopf subalgebra -- 9.2 Relative Hopf modules -- 9.3 When Hopf algebras free over their Hopf subalgebras -- 9.4 An example of a Hopf algebra which is not free over some Hopf subalgebra -- Chapter notes -- 10. Integrals -- 10.1 Definition of integrals for a bialgebra and its dual algebra -- 10.2 Existence and uniqueness of integrals for a Hopf algebra -- 10.3 Integrals and semisimplicity -- 10.4 Integrals and the trace function -- 10.5 Integrals and the antipode -- 10.6 Generalized integrals and grouplike elements -- 10.7 Integrals, the center, and cocommutative elements of the dual -- 10.8 Integrals and co-semisimplicity -- 10.9 Existence and uniqueness results for integrals of the dual algebra of a Hopf algebra -- Chapter notes -- 11. Actions by bialgebras and Hopf algebras -- 11.1 Monoidal categories -- 11.2 Module actions and module algebras, coalgebras -- 11.3 Comodule actions and comodule algebras, coalgebras -- 11.4 Duality between the smash product and smash coproduct -- 11.5 Prebraiding, braiding structures on a monoidal category -- 11.6 Yetter-Drinfel'd modules and biproducts -- 11.7 Abstract characterization of biproducts -- Chapter notes -- 12. Quasitriangular bialgebras and Hopf algebras -- 12.1 The quantum Yang-Baxter and braid equations, Yang- Baxter algebras."]
[{"$nulls":4},"12.2 Almost cocommutative Hopf algebras, quasitriangular bialgebras and Hopf algebras -- 12.3 Grouplike and ribbon elements -- 12.4 Factorizable Hopf algebras -- Chapter notes -- 13. The Drinfel'd double of a finite-dimensional Hopf algebra -- 13.1 The double and its category of representations -- 13.2 Basic properties of the double -- 13.3 Characterizations of the double as a quasitriangular Hopf algebra -- 13.4 The dual of the double -- 13.5 The double of a quasitriangular Hopf algebra -- 13.6 The double of a factorizable Hopf algebra -- 13.7 Quasi-ribbon and ribbon elements of the double -- 13.8 Generalized doubles and their duals -- Chapter notes -- 14. Coquasitriangular bialgebras and Hopf algebras -- 14.1 Coquasitriangular and Yang-Baxter coalgebras -- 14.2 Coquasitriangular bialgebras and Hopf algebras -- 14.3 The square of the antipode of a coquasitriangular Hopf algebra -- 14.4 The free coquasitriangular bialgebra on a coquasitriangular coalgebra -- Chapter notes -- 15. Pointed Hopf algebras -- 15.1 Crossed products -- 15.2 Pointed Hopf algebras as crossed products -- 15.3 Cocommutative pointed Hopf algebras -- the characteristic 0 case -- 15.4 Minimal-pointed Hopf algebras -- 15.5 Pointed Hopf algebras, biproducts, and Nichols algebras -- 15.6 Quantized enveloping algebras and their generalizations -- 15.7 Ore extensions and pointed Hopf algebras -- Chapter notes -- 16. Finite-dimensional Hopf algebras in characteristic 0 -- 16.1 Characterizations of semisimple Hopf algebras -- 16.2 Isomorphism types of Hopf algebras of the same dimension -- 16.3 Some very basic classification results -- Bibliography -- Index."]
[{"$nulls":3},"Sommario/riassunto","The book provides a detailed account of basic coalgebra and Hopf "]
[{"$nulls":4},"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."]