Quantizations of group actions

TL;DR

This paper classifies and explicitly constructs quantizations of monoidal categories of modules over finite groups, providing detailed examples for S3 and A4, and describing the quantizers as elements of the group algebra.

Contribution

It offers a complete classification of quantizations for modules over finite groups, with explicit formulas for S3 and A4, advancing understanding of group action quantizations.

Findings

Explicit quantizers for modules over S3 and A4

Complete classification of quantizations over finite groups

Quantizers expressed as elements of the group algebra

Abstract

We describe quantizations on monoidal categories of modules over finite groups. They are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over S3 and A4 we are given explicit forms for all quantizations.