Actions of Hopf algebras ∗

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. 

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

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

Forms of Coalgebras and Hopf Algebras

We study forms of coalgebras and Hopf algebras (i.e. coalgebras and Hopf algebras which are isomorphic after a suitable extension of the base field). We classify all forms of grouplike coalgebras according to the structure of their simple subcoalgebras. For Hopf algebras, given a W ∗-Galois field extension K ⊆ L for W a finite-dimensional semisimple Hopf algebra and a K-Hopf algebra H, we show ...

Coherent Unit Actions on Regular Operads and Hopf Algebras

J.-L. Loday introduced the concept of coherent unit actions on a regular operad and showed that such actions give Hopf algebra structures on the free algebras. Hopf algebras obtained this way include the Hopf algebras of shuffles, quasi-shuffles and planar rooted trees. We characterize coherent unit actions on binary quadratic regular operads in terms of linear equations of the generators of th...