Modules over quantum Laurent polynomials I

TL;DR

This paper investigates modules over quantum Laurent polynomials, establishing their tensor-minimal Gelfand--Kirillov dimension, determining the Brookes--Groves invariant for tensor products, and revealing the existence of nonholonomic simple modules.

Contribution

It introduces new results on the Gelfand--Kirillov dimension, Brookes--Groves invariant, and the existence of nonholonomic simple modules in the context of quantum Laurent polynomial modules.

Findings

Gelfand--Kirillov dimension is tensor-minimal for these modules

Brookes--Groves invariant is explicitly determined for tensor products

Nonholonomic simple modules can exist in this setting

Abstract

It is shown that the Gelfand--Kirillov dimension for modules over quantum Laurent polynomials is tensor-minimal. The Brookes--Groves invariant associated with a tensor product of modules is determined. It is also shown that there can be nonholonmic simple modules.