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Mathematics, Representation Theory, Algebraic Geometry
Abstract:
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.
