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Preprojective algebras, skew group algebras and Morita equivalences
- Publication Year :
- 2024
-
Abstract
- Let $\mathbb{K}$ 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 Schr\"{o}er. 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.<br />Comment: 21 pages
- Subjects :
- Mathematics - Representation Theory
16G20, 16S35, 16D90, 17B22
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.15049
- Document Type :
- Working Paper