Semi-Projective Representations and Twisted Representation Groups

2022/11/25 by Alessandro, Massimiliano, Gleissner, Christian, Kotonski, Julia
#Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Primary: 20C25 #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2211.14059

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.

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