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arXiv · 2108.00795

On deformed preprojective algebras

William Crawley-Boevey·Yuta Kimura
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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.

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William Crawley-Boevey, Yuta Kimura. 2021-08-02. On deformed preprojective algebras. https://arxiv.org/abs/2108.00795

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