On the homology of partial group actions

We study the partial group (co)homology of partial group actions using simplicial methods. We introduce the concept of universal globalization of a partial group action on a K-module and prove that, given a partial representation of G on M, the partial group homology Hᵖᵃʳ•(G, M) is naturally isomorphic to the usual group homology H•(G, KG ⊗_Gₚₐᵣ M), where KG ⊗_Gₚₐᵣ M is the universal globalization of the partial group action associated to M. We dualize this result into a cohomological spectral sequence converging to H•ₚₐᵣ(G,M).