The tilting theory of contraction algebras

August, J. (2020) The tilting theory of contraction algebras. Advances in Mathematics, 374, 107372. (doi: 10.1016/j.aim.2020.107372)

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To every minimal model of a complete local isolated cDV singularity Donovan–Wemyss associate a finite dimensional symmetric algebra known as the contraction algebra. We construct the first known standard derived equivalences between these algebras and then use the structure of an associated hyperplane arrangement to control the compositions, obtaining a faithful group action on the bounded derived category. Further, we determine precisely those standard equivalences which are induced by two-term tilting complexes and show that any standard equivalence between contraction algebras (up to algebra isomorphism) can be viewed as the composition of our constructed functors. Thus, for a contraction algebra, we obtain a complete picture of its derived equivalence class and, in particular, of its derived autoequivalence group.

Item Type:Articles
Glasgow Author(s) Enlighten ID:August, Dr Jenny
Authors: August, J.
College/School:University Services > Learning and Teaching Services Division
Journal Name:Advances in Mathematics
ISSN (Online):1090-2082
Published Online:27 August 2020

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