n‐representation‐finite algebras and twisted fractionally Calabi–Yau algebras

By Martin Herschend, Osamu Iyama. 2009

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In this 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 ℓ>0, twisted (n(ℓ−1)/ℓ)‐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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d386b9ea0365caf4f08ae577a310a6832064d0b4