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

TL;DR

This paper explores the relationship between n-representation-finite algebras and twisted fractionally Calabi-Yau properties, establishing their equivalence and providing new constructions via tensor products.

Contribution

It proves that all n-representation-finite algebras are twisted fractionally Calabi-Yau and characterizes certain twisted Calabi-Yau algebras as n-representation-finite, introducing a tensor product construction.

Findings

All n-representation-finite algebras are twisted fractionally Calabi-Yau.

Twisted Calabi-Yau algebras of certain dimensions are n-representation-finite.

A new construction method for n-representation-finite algebras using tensor products.

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.