On deformed preprojective algebras
Abstract
Deformed preprojective algebras are generalizations of the usual preprojective algebras introduced by Crawley-Boevey and Holland, which have applications to Kleinian singularities, the Deligne-Simpson problem, integrable systems and noncommutative geometry. In this paper we offer three contributions to the study of such algebras: (1) the 2-Calabi-Yau property; (2) the unification of the reflection functors of Crawley-Boevey and Holland with reflection functors for the usual preprojective algebras; and (3) the classification of tilting ideals in 2-Calabi-Yau algebras, and especially in deformed preprojective algebras for extended Dynkin quivers.
Cite
@article{arxiv.2108.00795,
title = {On deformed preprojective algebras},
author = {William Crawley-Boevey and Yuta Kimura},
journal= {arXiv preprint arXiv:2108.00795},
year = {2022}
}
Comments
The main changes are (1) the proof of the PBW property has been cut, as we can quote a theorem of He, Van Oystaeyen and Zang and (2) the proof of Theorem 1.7 has been expanded, filling a small gap in the corresponding theorem by Buan, Iyama, Reiten and Scott