Preprojective algebras, skew group algebras and Morita equivalences

2024/06/21 by Xiao-Wu Chen, Ren Wang, Chen, Xiao-Wu +1
Computer Science · Mathematics · #16D90 #16G20 #16S35 #17B22 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2406.15049

openalex publication_date 2024/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbbK be a field of characteristic p and G be a cyclic p-group which acts on a finite acyclic quiver Q. The folding process associates a Cartan triple to the action. We establish a Morita equivalence between the skew group algebra of the preprojective algebra of Q and the generalized preprojective algebra associated to the Cartan triple in the sense of Geiss, Leclerc and Schröer. The Morita equivalence induces an isomorphism between certain ideal monoids of these preprojective algebras, which is compatible with the embedding of Weyl groups appearing in the folding process.

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• Mutation of representations and nearly Morita equivalence
• Galois coverings, Morita equivalence and smash extensions of categories over a field
• Quivers with potentials and actions of finite abelian groups