The Cohen-Macaulay Auslander algebras of string algebras
Yu-Zhe Liu, Chao Zhang

TL;DR
This paper explicitly constructs Cohen-Macaulay Auslander algebras for string algebras, explores their finiteness properties, and characterizes gentle algebras' self-injective dimension through these algebras.
Contribution
It provides an explicit construction of Cohen-Macaulay Auslander algebras for string algebras and links their representation-finiteness to that of the original algebras.
Findings
Cohen-Macaulay Auslander algebras are explicitly constructed for string algebras.
Representation-finiteness of certain string algebras is characterized via their Cohen-Macaulay Auslander algebras.
Self-injective dimension of gentle algebras is characterized using Cohen-Macaulay Auslander algebras.
Abstract
The Cohen-Macaulay Auslander algebra of any string algebra is explicitly constructed in this paper. Furthermore, we show that a class of special string algebras, which are called to be string algebras with G-condition, are representation-finite if and only if their Cohen-Macaulay Auslander algebras are representation-finite. Finally, the self-injective dimension of gentle algebras is characterized using their Cohen-Macaulay Auslander algebras.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics
