n-representation-finite algebras and n-APR tilting

Abstract

We introduce the notion of n-representation-finiteness, generalizing representation-finite hereditary algebras. We establish the procedure of n-APR tilting, and show that it preserves n-representation-finiteness. We give some combinatorial description of this procedure, and use this to completely describe a class of n-representation-finite algebras called "type A".

33 pages, Sections 3 and 4 rearranged, Subsection 3.3 generalized, some explanations added and typos corrected

References in corpus (7)

• n-representation-finite algebras and twisted fractionally Calabi-Yau algebras
• Deformed Calabi-Yau Completions
• Stable categories of higher preprojective algebras
• Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories
• Trivial Maximal 1-Orthogonal Subcategories For Auslander's 1-Gorenstein Algebras
• Almost $\mathcal{D}$-split sequences and derived equivalences
• From iterated tilted algebras to cluster-tilted algebras

Cited by in corpus (4)

• n-representation-finite algebras and twisted fractionally Calabi-Yau algebras
• Stable categories of higher preprojective algebras
• Projectively generated $d$-abelian categories are $d$-cluster tilting
• Cluster tilting for higher Auslander algebras