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arXiv · 1903.02107

The Bogomolov-Tian-Todorov Theorem Of Cyclic $A_\infty$-Algebras

Junwu Tu
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Abstract

Let $A$ be a finite-dimensional smooth unital cyclic $A_\infty$-algebra. Assume furthermore that $A$ satisfies the Hodge-to-de-Rham degeneration property. In this short note, we prove the non-commutative analogue of the Bogomolov-Tian-Todorov theorem: the deformation functor associated with the differential graded Lie algebra of Hochschild cochains of $A$ is smooth. Furthermore, the deformation functor associated with the DGLA of cyclic Hochschild cochains of $A$ is also smooth.

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Junwu Tu. 2019-03-05. The Bogomolov-Tian-Todorov Theorem Of Cyclic $A_\infty$-Algebras. https://arxiv.org/abs/1903.02107

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