On Projective Representations of Finitely Generated Groups

TL;DR

This paper characterizes monomial projective representations of finitely generated nilpotent groups and identifies conditions under which polycyclic groups have finite-dimensional projective representations.

Contribution

It provides a new characterization of monomial projective representations and classifies polycyclic groups with finite-dimensional projective representations.

Findings

Characterization of monomial projective representations of finitely generated nilpotent groups

Identification of polycyclic groups with finite-dimensional projective representations

Advancement in understanding the structure of projective representations in group theory

Abstract

We prove a characterization of monomial projective representations of finitely generated nilpotent groups. We also characterize polycyclic groups whose projective representations are finite dimensional.