Projective representations of Heisenberg groups over the rings of order 𝑝<sup>2</sup>-Reference-Cited by-同舟云学术

Projective representations of Heisenberg groups over the rings of order 𝑝²

Published:2023-06-27 Issue:0 Volume:0 Page:
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Hatui Sumana¹,Narayanan E. K.²,Singla Pooja³

Affiliation:

1. School of Mathematical Sciences , National Institute of Science Education and Research , An OCC of Homi Bhabha National Institute , Bhubaneswar 752050, Odisha , India

2. Department of Mathematics , Indian Institute of Science , Bangalore 560012 , India

3. Department of Mathematics and Statistics , Indian Institute of Technology Kanpur , Kanpur 208016 , India

Abstract

Abstract We describe the 2-cocycles, Schur multiplier and representation group of discrete Heisenberg groups over the unital rings of order p 2

p^{2}

. We also describe all projective representations of Heisenberg groups with entries from the rings Z / p 2 ⁢ Z

\mathbb{Z}/p^{2}\mathbb{Z}

and F p ⁢ [ t ] / ( t 2 )

\mathbb{F}_{p}[t]/(t^{2})

for odd primes 𝑝 and obtain a classification of their degenerate and non-degenerate 2-cocycles.

Funder

Indian Institute of Science

Science and Engineering Research Board

Ministry of Education, India

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2022-0033/pdf

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