Frobenius-Perron theory of representation-directed algebras. (English) Zbl 1541.16016
The authors study the Frobenius-Perron dimension of representation-directed algebras and quotient algebras of canonical algebras of type ADE, prove that the Frobenius-Perron dimension of a representation-directed algebra is always zero and the Frobenius-Perron dimension of a quotient algebra of canonical algebras of type ADE is 0 or 1. They also give a sufficient and necessary condition for a quotient algebra of a canonical algebra of type ADE under which its Frobenius-Perron dimension is 0.
Reviewer: Mee Seong Im (Annapolis)
MSC:
| 16G60 | Representation type (finite, tame, wild, etc.) of associative algebras |
| 16G70 | Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers |
Keywords:
Frobenius-Perron dimension; endofunctor; representation-directed algebra; canonical algebraReferences:
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