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|Title: ||Deformed Calabi-Yau completions|
|Authors: ||Keller, Bernhard|
VAN DEN BERGH, Michel
|Issue Date: ||2011|
|Publisher: ||WALTER DE GRUYTER & CO|
|Citation: ||JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 654. p. 125-180|
|Abstract: ||We define and investigate deformed n-Calabi-Yau completions of homologically smooth differential graded (=dg) categories. Important examples are: deformed preprojective algebras of connected non-Dynkin quivers, Ginzburg dg algebras associated to quivers with potentials and dg categories associated to the category of coherent sheaves on the canonical bundle of a smooth variety. We show that deformed Calabi-Yau completions do have the Calabi-Yau property and that their construction is compatible with derived equivalences and with localizations. In particular, Ginzburg dg algebras have the Calabi-Yau property. We show that deformed 3-Calabi-Yau completions of algebras of global dimension at most 2 are quasi-isomorphic to Ginzburg dg algebras and apply this to the study of cluster-tilted algebras and to the construction of derived equivalences associated to mutations of quivers with potentials. In the appendix, Michel Van den Bergh uses non-commutative differential geometry to give an alternative proof of the fact that Ginzburg dg algebras have the Calabi-Yau property.|
|Notes: ||[Keller, Bernhard] Univ Paris 07, Inst Math Jussieu, UFR Math, CNRS,UMR 7586, F-75205 Paris 13, France. [Van den Bergh, Michel] Hasselt Univ, Dept WNI, B-3590 Diepenbeek, Belgium.
|ISI #: ||000290377000003|
|Type: ||Journal Contribution|
|Validation: ||ecoom, 2012|
|Appears in Collections: ||Research publications|
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