Semi-Projective Representations and Twisted Representation Groups

TL;DR

This paper extends the concept of representation groups to semi-projective representations over algebraically closed fields and provides an algorithm to compute all such twisted groups for finite groups.

Contribution

It introduces the notion of semi-projective representations and develops a computer algorithm to find all associated twisted representation groups.

Findings

Algorithm successfully computes all semi-projective twisted groups for finite groups.

Extension of Schur's representation group concept to semi-projective case.

Provides a systematic method for analyzing semi-projective representations.

Abstract

A semi-projective representation is a homomorphism of a finite group into the group of semi-projective transformations of a finite dimensional vector space over a field. Schur's concept of a representation group for projective representations is extended to semi-projective representations under the assumption that the field is algebraically closed. A computer algorithm is given that produces, for a given finite group, all such twisted representation groups under trivial or conjugation actions on the field of complex numbers.