Stabilizer for Hopf Algebra Actions

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

Adjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.

For a Hopf algebra H over a commutative ring k and a left H-module V, the tensor endofunctors V k - and - kV are left adjoint to some kinds of  Hom-endofunctors of _HM. The units and counits of these adjunctions are formally trivial as in the classical case.The category of (bi-) modules over a quasi-Hopf algebra is monoidal and some generalized versions of  Hom-tensor relations have been st...

A note on the new basis in the mod 2 Steenrod algebra

‎The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations‎, ‎denoted by $Sq^n$‎, ‎between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space‎. ‎Regarding to its vector space structure over $mathbb{Z}_2$‎, ‎it has many base systems and some of the base systems can also be restricted to its sub algebras‎. ‎On the contrary‎, ‎in ...

Hopf Algebras in Quantum Computation

In this thesis, we use string diagrams to study the theory of Hopf algebras in the context of Categorical Quantum Mechanics. First, we treat the theory of representations of a Hopf algebra diagrammatically. The category of representations of a quasitriangular Hopf algebra Rep(H) is a braided tensor category and can be understood as a process theory of particles in Topological Quantum theory. We...