Calabi-Yau completions and orbifold equivalences

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 $X$.

47 pages; v2: added an assumption on lifting dg module structures

References in corpus (2)

• Calabi-Yau algebras
• On Serre duality for compact homologically smooth DG algebras

Cited by in corpus (5)

• Notes on generalized global symmetries in QFT
• Orbifolds of n-dimensional defect TQFTs
• 3-dimensional defect TQFTs and their tricategories
• Lecture notes on 2-dimensional defect TQFT
• Orbifolds by 2-groups and decomposition