Projective representations of Heisenberg groups over the rings of order p^2

TL;DR

This paper classifies projective representations and 2-cocycles of discrete Heisenberg groups over rings of order p^2, providing a detailed analysis of their Schur multipliers and representation groups.

Contribution

It offers a comprehensive description of 2-cocycles, Schur multipliers, and projective representations for Heisenberg groups over specific rings of order p^2, including classifications of degenerate and non-degenerate cases.

Findings

Classification of all projective representations over specified rings

Explicit description of 2-cocycles and Schur multipliers

Analysis of degenerate and non-degenerate cocycles

Abstract

In this article we describe the 2-cocycles, Schur multiplier and representation group of discrete Heisenberg groups over the unital rings of order $p^2$. We describe all projective representations of Heisenberg groups with entries from the rings $\mathbb Z/p^2\mathbb Z$ and $\mathbb{F}_p[t]/(t^2)$ and obtain a classification of their degenerate and non-degenerate 2-cocycles.