Twisted quantum Drinfeld Hecke algebras

TL;DR

This paper extends quantum Drinfeld Hecke algebras by including a 2-cocycle, classifies these algebras for specific groups, and explores how twisting affects their parameter spaces and deformations.

Contribution

It introduces twisted quantum Drinfeld Hecke algebras, connects them to Hochschild cohomology, and provides classifications for diagonal and symmetric group actions.

Findings

Parameter space for symmetric groups is reduced in the twisted setting.

Twisted algebras are specializations of deformations of twisted skew group algebras.

Explicit classification results for diagonal actions and symmetric groups.

Abstract

We generalize quantum Drinfeld Hecke algebras by incorporating a 2-cocycle on the associated finite group. We identify these algebras as specializations of deformations of twisted skew group algebras, giving an explicit connection to Hochschild cohomology. We classify these algebras for diagonal actions, as well as for the symmetric groups with their natural representations. Our results show that the parameter spaces for the symmetric groups in the twisted setting is smaller than in the untwisted setting.