Tate cohomology of finite dimensional Hopf algebras
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ABSTRACT......Page 2 DEDICATION......Page 3 ACKNOWLEDGEMENTS......Page 4 TABLE OF CONTENTS......Page 5 INTRODUCTION......Page 7 Hopf algebras......Page 11 Homological algebra......Page 16 Products in cohomology......Page 18 Yoneda product......Page 19 Tensor product of projective resolutions......Page 20 Notation and conventions......Page 24 TATE AND TATE-HOCHSCHILD COHOMOLOGY......Page 26 Tate cohomology for finite dimensional Hopf algebras......Page 27 Definition of Tate cohomology......Page 28 Properties of Tate cohomology......Page 29 Tate-Hochschild cohomology for finite dimensional Hopf algebras......Page 30 Cup product on Tate cohomology......Page 31 Cup product on Tate-Hochschild cohomology......Page 33 Relationship between the Tate and Tate-Hochschild cohomology rings of A......Page 36 Tate cohomology of Taft algebra......Page 39 Tate-Hochschild cohomology of Taft algebra......Page 43 Tate-Hochschild cohomology of a group algebra......Page 48 Agreement of products......Page 49 Reduction to Tate cohomology and relations with subgroups......Page 50 Decomposition of the Tate-Hochschild cohomology......Page 52 Products in negative Tate-Hochschild cohomology......Page 59 The dihedral group of order 8......Page 61 The symmetric group on three elements......Page 63 FINITE GENERATION OF TATE COHOMOLOGY......Page 68 Modules with bounds in finitely generated submodules......Page 69 Modules with finitely generated Tate cohomology......Page 77 Radford's algebra......Page 81 The restricted enveloping algebra of sl2(k)......Page 83 SUMMARY......Page 86 REFERENCES......Page 88
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