viii CONTENT S 4.3 Trac e function s an d affin e invariants : th e non-co m mutative case 4 5 4.4 Ideal s i n A#H an d A a s a n A^-modul e 4 8 4.5 A Morit a contex t relatin g A#H an d A H 5 2 Chapter 5 . Coradical s an d Filtration s 5 6 5.1 Simpl e subcoalgebra s an d th e coradica l 5 6 5.2 Th e coradica l filtration 6 0 5.3 Injectiv e coalgebr a map s 6 5 5.4 Th e coradica l filtratio n o f pointe d coalgebra s 6 7 5.5 Examples : t/(g ) an d U q (g) 7 3 5.6 Th e structur e o f pointe d cocommutativ e Hop f algebra s 7 6 5.7 Semisimpl e cocommutativ e connecte d Hop f algebra s 8 3 Chapter 6 . Inne r Action s 8 7 6.1 Definition s an d example s 8 7 6.2 A Skolem-Noethe r theore m fo r Hop f algebra s 8 9 6.3 Maxima l inne r subcoalgebra s 9 2 6.4 X-inne r action s an d extendin g t o quotient s 9 6 Chapter 7 . Crosse d product s 10 1 7.1 Definition s an d example s 10 1 7.2 Clef t extension s an d existenc e o f crosse d product s 10 5 7.3 Inne r action s an d equivalenc e o f crosse d product s 11 2 7.4 Generalize d Maschk e theorem s an d semiprim e crosse d products 11 6 7.5 Twiste d //-comodul e algebra s 12 1 Chapter 8 . Galoi s Extension s 12 3 8.1 Definitio n an d example s 12 3 8.2 Th e norma l basi s propert y an d clef t extension s 12 8 8.3 Galoi s extension s fo r finite-dimensional H 13 1 8.4 Norma l base s an d Hop f algebr a quotient s 13 9 8.5 Relativ e Hop f module s 14 4
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