Representations of the quantum torus and applications to finitely presented groups

TL;DR

This paper establishes a structure theorem for strongly holonomic modules over quantum tori and applies it to understand finitely presented abelian-by-nilpotent groups.

Contribution

It introduces a new structure theorem for modules over quantum tori and applies it to classify certain finitely presented groups.

Findings

Structure theorem for strongly holonomic modules over quantum tori

Application to finitely presented abelian-by-nilpotent groups

Enhanced understanding of group representations in quantum algebra

Abstract

A structure theorem is proved for strongly holonomic modules over a quantum torus (a crossed product of a field with a free abelian group in which the field is central). This can be applied to give a structure theorem for finitely presented abelian-by-nilpotent groups.