Total preprojective algebras

Le résumé fourni par la source

Abstract We introduce total preprojective algebras $\Psi $ of path algebras of Dynkin quivers $kQ$ and prove that they are isomorphic to $2$-Auslander algebras of preprojective algebras $\Pi $ of $kQ$. In particular, $\Psi $ has global dimension $3$ and dominant dimension $3$. We also describe $\Psi $ as a tensor algebra of a certain explicit bimodule over the Auslander algebra of $kQ$. As an application, we give a presentation of $\Psi $ by explicit quivers with relations. More generally, we introduce total $(d+1)$-preprojective algebras of $d$-representation finite algebras and give all the corresponding results.

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