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arXiv · 1509.00880

Calabi-Yau completions and orbifold equivalences

Nils Carqueville·Alexander Quintero Velez
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Abstract

Calabi-Yau algebras are particularly symmetric differential graded algebras. There is a construction 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 $X$ with invertible quantum dimensions between them. Any such relation entails a whole family of equivalences between categories. We show that an orbifold equivalence between two homologically smooth and proper dg algebras lifts to an orbifold equivalence between their Calabi-Yau completions under certain conditions on $X$.

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BibTeXRIS

Nils Carqueville, Alexander Quintero Velez. 2019-08-23. Calabi-Yau completions and orbifold equivalences. https://arxiv.org/abs/1509.00880

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