We have the equivariant cohomology theory in topology/geometry, when the topological space has a group action, equivariant cohomology is a functor that reflects both the topology of the space and the action of the group. For an introduction please see the wiki page for equivariant cohomology. On the other hand, for associative algebra we have Hochschild cohomology see the nLab page and for commutative asscociative algebra we have Harrison cohomology, which are algebraic formalisms. Naturally, a question is, if we have a (group) twisted algebra, do we have the similar studies of equivariant Hochschild/Harrison (co)homology? If so, could anyone provide some references? I simply did not find anything like this myself. If not, what creates the (obvious) obstruction when studying? Thanks ahead!
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