Cosovereign Hopf algebras

Cohomological Dimensions of Universal Cosovereign Hopf Algebras

We compute the Hochschild and Gerstenhaber-Schack cohomological dimensions of the universal cosovereign Hopf algebras, when the matrix of parameters is a generic asymmetry. Our main tools are considerations on the cohomologies of free product of Hopf algebras, and on the invariance of the cohomological dimensions under graded twisting by a finite abelian group.

Hopf algebras having a dense big cell

We discuss some axioms that ensure that a Hopf algebra has its simple comodules classified using an analogue of the Borel–Weil construction. More precisely we show that a Hopf algebra having a dense big cell satisfies to the above requirement. This method has its roots in the work of Parshall and Wang in the case of q-deformed quantum groups GL and SL. Here we examine the example of universal c...

On the Coderivations of Some Hopf Algebras

NOTES ON REGULAR MULTIPLIER HOPF ALGEBRAS

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

Gorenstein global dimensions for Hopf algebra actions

Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra‎. ‎In this paper‎, ‎we investigate Gorenstein global dimensions for Hopf‎ ‎algebras and twisted smash product algebras $Astar H$‎. ‎Results from‎ ‎the literature are generalized‎.