Cohen-Macaulay Auslander algebras of gentle algebras

Abstract

For any gentle algebra $\Lambda =KQ/⟨I⟩$, following Kalck, we describe the quiver and the relations for its Cohen-Macaulay Auslander algebra $\mathrm{Aus}(\mathrm{Gproj}\Lambda )$ explicitly, and obtain some properties, such as $\Lambda$ is representation-finite if and only if $\mathrm{Aus}(\mathrm{Gproj}\Lambda )$ is; if $Q$ has no loop and any indecomposable $\Lambda$-module is uniquely determined by its dimension vector, then any indecomposable $\mathrm{Aus}(\mathrm{Gproj}\Lambda )$-module is uniquely determined by its dimension vector.

17 pages

References in corpus (5)

• On triangulated orbit categories
• Singularity categories of gentle algebras
• Perverse equivalences, BB-tilting, mutations and applications
• Gentle algebras arising from surface triangulations
• Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D

Cited by in corpus (2)

• On Cohen-Macaulay Auslander algebras
• Desingularization of quiver Grassmannians for Gentle algebras