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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11965

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. keller@math.jussieu.fr; vdbergh@luc.ac.be
URI: http://hdl.handle.net/1942/11965
DOI: 10.1515/CRELLE.2011.031
ISI #: 000290377000003
ISSN: 0075-4102
Category: A1
Type: Journal Contribution
Validation: ecoom, 2012
Appears in Collections: Research publications

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