Partial cohomology of groups

TL;DR

This paper introduces a new cohomology theory for groups based on partial actions, linking it to the partial Schur multiplier and inverse semigroup cohomology.

Contribution

It develops a novel cohomology framework for groups using partial actions, connecting it with existing algebraic structures.

Findings

Establishes a relationship between partial group cohomology and the partial Schur multiplier.

Links partial group cohomology with cohomology of inverse semigroups.

Provides foundational results for further exploration of partial symmetries in algebra.

Abstract

We develop a cohomology theory of groups based on partial actions and explore its relation with the partial Schur multiplier as well as with cohomology of inverse semigroups.