On $n$-hereditary algebras and $n$-slice algebras

Jin Yun Guo; Yanping Hu

On $n$-hereditary algebras and $n$-slice algebras

Representation Theory 2024-07-12 v3 Rings and Algebras

Authors: Jin Yun Guo , Yanping Hu

Abstract

In this paper we show that acyclic $n$ -slice algebras are exactly acyclic $n$ -hereditary algebras whose $(n+1)$ -preprojective algebras are $(q+1,n+1)$ -Koszul. We also list the equivalent triangulated categories arising from the algebra constructions related to an $n$ -slice algebra. We show that higher slice algebras of finite type appear in pairs and they share the Auslander-Reiten quiver for their higher preprojective components.

Keywords

n-hereditary algebras n-slice algebras preprojective algebras koszul algebras triangulated categories auslander-reiten quiver

Cite

@article{arxiv.2204.06879,
  title  = {On $n$-hereditary algebras and $n$-slice algebras},
  author = {Jin Yun Guo and Yanping Hu},
  journal= {arXiv preprint arXiv:2204.06879},
  year   = {2024}
}

On $n$-hereditary algebras and $n$-slice algebras

Abstract

Keywords

Cite

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