Schur's theory for partial projective representations

TL;DR

This paper extends Schur's theory to partial projective representations by developing a partial cohomology framework and describing the partial Schur multiplier, linking it to partial group actions.

Contribution

It introduces a second partial cohomology group relative to an ideal and an analogue of central extension for partial actions, unifying with existing partial cohomology theories.

Findings

Defined the partial Schur multiplier comprehensively.

Established a consistent partial cohomology framework.

Connected partial cohomology with classical Schur theory.

Abstract

This article focuses on those aspects about partial actions of groups which are related to Schur's theory on projective representations. It provides an exhaustive description of the partial Schur multiplier, and this result is achieved by introducing the concept of a second partial cohomology group relative to an ideal, together with an appropriate analogue of a central extension. In addition, the new framework is proved to be consistent with the earlier notion of cohomology over partial modules.