A module structure on Hochschild cohomology of coideal subalgebras (Q6179269)

Let us recall that the relation between a Hopf algebra and its Hopf subalgebra is a fundamental research topic. In this work, the authors first review the basic definitions. They obtain a characterisation of faithful flatness as well as homological results. Then they consider a right coideal subalgebra of a Hopf algebra \(H\) and construct a left \(H^*\)-module structure on the Hochschild cohomology of \(B\) with coefficients in \(B \bigotimes M\) where \(M\) is a \(B\)-module and a right \(H\)-comodule satisfying a compatible condition.