Homotopy Cartan calculus and inner deformations of $A_\infty$-algebras

Alexey A. Sharapov; Evgeny D. Skvortsov

paper

Homotopy Cartan calculus and inner deformations of $A_{\infty}$ -algebras

arXiv:2202.10925

Abstract

We consider inner deformations of families of $A_{\infty}$ -algebras. With the help of noncommutative Cartan's calculus, we prove the invariance of Hochschild (co)homology under inner deformations. The invariance also holds for cyclic cohomology classes that satisfy some additional conditions. Applications to dg-algebras and QFT problems are briefly discussed.

arXiv comment29 pages; v2- journal version

Homotopy Cartan calculus and inner deformations of A∞​-algebras

Abstract

Homotopy Cartan calculus and inner deformations of $A_{\infty}$ -algebras