Homotopy Cartan calculus and inner deformations of $$A_\infty $$-algebras
Copyright policy )Homotopy Cartan calculus and inner deformations of $$A_\infty $$-algebras
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.
29 pages; v2- journal version
- National Research University of Electronic Technology Russian Federation
- P.N. Lebedev Physical Institute of the Russian Academy of Sciences Russian Federation
- Tomsk State Pedagogical University Russian Federation
- University of Mons Belgium
A∞-алгебры, Nonassociative algebras satisfying other identities, deformation of \(A_{\infty}\)-algebras, FOS: Physical sciences, Mathematical Physics (math-ph), 16S80, 17A30, некоммутативное дифференциальное исчисление, Хохшильда когомологии, higher-spin symmetry, Deformations of associative rings, Mathematics - Quantum Algebra, FOS: Mathematics, Hochschild and cyclic cohomology, Quantum Algebra (math.QA), циклические когомологии, noncommutative differential calculus, Mathematical Physics
A∞-алгебры, Nonassociative algebras satisfying other identities, deformation of \(A_{\infty}\)-algebras, FOS: Physical sciences, Mathematical Physics (math-ph), 16S80, 17A30, некоммутативное дифференциальное исчисление, Хохшильда когомологии, higher-spin symmetry, Deformations of associative rings, Mathematics - Quantum Algebra, FOS: Mathematics, Hochschild and cyclic cohomology, Quantum Algebra (math.QA), циклические когомологии, noncommutative differential calculus, Mathematical Physics
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