Total preprojective algebras
Abstract
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.
Fields of Study & Subjects
Logic
programming
and type systems
Advanced Algebra and Logic
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 11
- Publication date
- 7 May 2026
- Language
- EN