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Article overview
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Calabi-Yau completions and orbifold equivalences | Nils Carqueville
; Alexander Quintero Velez
; | Date: |
2 Sep 2015 | Abstract: | Calabi-Yau algebras are particularly symmetric differential graded algebras.
There is a construction due to Keller called ’Calabi-Yau completion’ which
produces a canonical Calabi-Yau algebra from any homologically smooth dg
algebra.
Homologically smooth dg algebras also form a 2-category to which the
construction of ’equivariant completion’ can be applied. In this theory two
objects are called ’orbifold equivalent’ if there is a 1-morphism with
invertible quantum dimensions between them. Any such relation entails a whole
family of equivalences between categories.
We show that Calabi-Yau completion and equivariant completion are compatible.
More precisely, we prove that any orbifold equivalence between two
homologically smooth and proper dg algebras lifts to an orbifold equivalence
between their Calabi-Yau completions. As a corollary we obtain orbifold
equivalences between Ginzburg algebras of Dynkin quivers. | Source: | arXiv, 1509.0880 | Services: | Forum | Review | PDF | Favorites |
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