n-representation-finite algebras and twisted fractionally Calabi-Yau algebras

Abstract

In this short paper, we study $n$-representation-finite algebras from the viewpoint of the fractionally Calabi-Yau property. We shall show that all $n$-representation-finite algebras are twisted fractionally Calabi-Yau. We also show that for any $\ell >0$, twisted $\frac{n(\ell -1)}{\ell }$-Calabi-Yau algebras of global dimension at most $n$ are $n$-representation-finite. As an application, we give a construction of $n$-representation-finite algebras using the tensor product.

15 pages, more detailed proofs and examples are added

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• Classification of the d-representation-finite symmetric k-algebras of finite representation type