Cohomology theories of Hopf bimodules and cup-product (Q2712600)

The category of Hopf bimodules over a finite dimensional Hopf algebra \(A\) is known to be equivalent to a category of modules over a ring. The particular ring chosen here is \(X:=(A^{*op}\otimes A^*)\otimes(A\otimes A^{op})\) with a multiplication that comes from the quantum double of \(A\). Certain cohomology theories of Hopf bimodules (Gerstenhaber-Schack, Ospel) are found to be described by the Ext-functor of \(X\)-modules. The (Yoneda) cup-product on Ext is transferred to an explicit formula for the cup product of the Hopf bimodule cohomology theories.