The stable AR-quiver of a quantum complete intersection

TL;DR

This paper characterizes the structure of the stable Auslander-Reiten quiver for quantum complete intersections, revealing specific tree classes depending on the algebra's representation type, with implications for understanding their module categories.

Contribution

It provides a complete description of the tree classes of components of the stable Auslander-Reiten quiver for quantum complete intersections, including the wild and tame cases.

Findings

All wild type cases have tree class A_infinity.

Tame cases have one component with tree class latA_{12} and others with A_infinity.

The structure of the quiver components depends on the algebra's representation type.

Abstract

We completely describe the tree classes of the components of the stable Auslander-Reiten quiver of a quantum complete intersection. In particular, we show that the tree class is always $A_{\infty}$ whenever the algebra is of wild representation type. Moreover, in the tame case, there is one component of tree class $\tilde{A}_{12}$, whereas all the other are of tree class $A_{\infty}$.