2025/02/07 by Chan, Aaron, Iyama, Osamu, Marczinzik, Rene
#16G10 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2502.04683
We introduce total preprojective algebras Ψ of path algebras of Dynkin quivers kQ, and prove that they are isomorphic to 2-Auslander algebras of preprojective algebras Π of kQ. In particular, Ψ has global dimension 3 and dominant dimension 3. We also describe Ψ as a tensor algebra of a certain explicit bimodule over the Auslander algebra of kQ. As an application, we give a presentation of Ψ 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.