Cohomology of partial smash products
  We define the partial group cohomology as the right derived functor of the functor of partial invariants, we relate this cohomology with partial derivations and with the partial augmentation ideal and we show that there exists a Grothendieck spectral sequence relating cohomology of partial smash algebras with partial group cohomology and algebra cohomology. 
Edson Ribeiro Alvares, Marcelo Muniz Alves and Maria Julia Redondo
math.RA