Homotopy Cartan calculus and inner deformations of $A_\infty$-algebras
Alexey A. Sharapov, Evgeny D. Skvortsov
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Abstract
We consider inner deformations of families of -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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra