Calabi-Yau structures on Drinfeld quotients and Amiot's conjecture
Bernhard Keller, Junyang Liu
TL;DR
This paper extends Amiot's 2009 construction of Calabi-Yau structures to the dg setting and uses it to outline a proof of her conjecture regarding 2-Calabi-Yau triangulated categories with cluster-tilting objects.
Contribution
It introduces a dg version of Amiot's construction and applies it to prove her conjecture on 2-Calabi-Yau categories.
Findings
Extended Calabi-Yau structures to dg categories
Provided an outline for proving Amiot's conjecture
Connected Verdier quotients with Calabi-Yau properties
Abstract
In 2009, Claire Amiot gave a construction of Calabi-Yau structures on Verdier quotients. We sketch how to lift it to the dg setting. We use this construction as an important step in an outline of the proof of her conjecture on the structure of 2-Calabi-Yau triangulated categories with a cluster-tilting object.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology