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- W2971389732 abstract "We introduce the Hochschild extensions of dg algebras, which are $A_infty$-algebras. We show that all exact Hochschild extensions are symmetric Hochschild extensions, more precisely, every exact Hochschild extension of a finite dimensional complete typical dg algebra is a symmetric $A_infty$-algebra. Moreover, we prove that the Koszul dual of trivial extension is Calabi-Yau completion and the Koszul dual of exact Hochschild extension is deformed Calabi-Yau completion, more precisely, the Koszul dual of the trivial extension of a finite dimensional complete dg algebra is the Calabi-Yau completion of its Koszul dual, and the Koszul dual of an exact Hochschild extension of a finite dimensional complete typical dg algebra is the deformed Calabi-Yau completion of its Koszul dual." @default.
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- W2971389732 date "2019-09-05" @default.
- W2971389732 modified "2023-09-26" @default.
- W2971389732 title "Exact Hochschild extensions and deformed Calabi-Yau completions" @default.
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