| In the first three chapters of this thesis we recall basics of Hopf algebras, cyclic cohomology and braided monoidal categories.;In Chapter five, we define a super version of Connes-Moscovici Hopf algebra H1 [9]. For that we define a super-bicrossproduct Hopf algebra kGs2 ▸ ◃U gs1 , analogous to the non super case [9, 17]. We call this super-bicrossproduct Hopf algebra the super version of H1 and denote it by Hs1 .;Keywords. Noncommutative geometry, Hopf algebra, braided monoidal categories, Hopf cyclic cohomology, super mathematics.;Chapters four and five form the heart of this thesis. In Chapter four, we extend the whole theory of Hopf cyclic cohomology with coefficients [18, 19, 25, 26], to symmetric braided monoidal abelian categories. We also obtain a braided version of Connes-Moscovici's Hopf cyclic cohomology [9, 10, 11] in any (not necessarily symmetric) braided monoidal abelian category. We use our theory to define a Hopf cyclic cohomology for super Hopf algebras and for quasitriangular quasi-Hopf algebras. |
