The Twisted Partial Group Algebra and (Co)homology of Partial Crossed Products.

Given a group G and a partial factor set σ of G, we introduce the twisted partial group algebra κ par σ G , which governs the partial projective σ -representations of G into algebras over a field κ. Using the relation between partial projective representations and twisted partial actions we endow κ par σ G with the structure of a crossed product by a twisted partial action of G on a commutative subalgebra of κ par σ G. Then, we use twisted partial group algebras to obtain a first quadrant Grothendieck spectral sequence converging to the Hochschild homology of the crossed product A ∗ Θ G , involving the Hochschild homology of A and the partial homology of G, where Θ is a unital twisted partial action of G on a κ -algebra A with a κ -based twist. An analogous third quadrant cohomological spectral sequence is also obtained. [ABSTRACT FROM AUTHOR]