Cohomology of partial smash products

TL;DR

This paper introduces partial group cohomology via derived functors, explores its connections with partial derivations and augmentation ideals, and establishes a spectral sequence linking cohomologies of partial smash algebras, partial groups, and algebras.

Contribution

It defines partial group cohomology as a derived functor, relates it to partial derivations and augmentation ideals, and constructs a spectral sequence connecting various cohomologies.

Findings

Defined partial group cohomology as a right derived functor.

Connected partial cohomology with partial derivations and augmentation ideals.

Established a Grothendieck spectral sequence relating cohomologies.

Abstract

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.