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arXiv · 1909.02200

Exact Hochschild extensions and deformed Calabi-Yau completions

Yang Han·Xin Liu·Kai Wang
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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.

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Yang Han, Xin Liu, Kai Wang. 2019-09-05. Exact Hochschild extensions and deformed Calabi-Yau completions. https://arxiv.org/abs/1909.02200

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