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arXiv · 2502.04683

Total preprojective algebras

Aaron Chan·Osamu Iyama·Rene Marczinzik
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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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Aaron Chan, Osamu Iyama, Rene Marczinzik. 2025-02-07. Total preprojective algebras. https://arxiv.org/abs/2502.04683

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