Modules of constant Jordan type over quantum complete intersections

TL;DR

This paper introduces the concept of modules with constant Jordan type over quantum complete intersections, explores their properties, invariance under Auslander-Reiten components, and classifies specific stable types in the two-generator case.

Contribution

It is the first to study constant Jordan type modules over quantum complete intersections, establishing foundational properties and classification results.

Findings

Constant Jordan type is an invariant of Auslander-Reiten components.

Classification of modules with stable constant Jordan type [1] or [n-1] in the 2-generator case.

Basic properties of modules of constant Jordan type over these algebras.

Abstract

We initiate the study of modules of constant Jordan type for quantum complete intersections, and prove a range of basic properties. We then show that for these algebras, constant Jordan type is an invariant of Auslander-Reiten components. Finally, we classify modules with stable constant Jordan type [1] or [n-1] in the 2-generator case.