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Cup product on A-infinity cohomology and deformations

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Skvortsov,  Evgeny D.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1901.07872.pdf
(Preprint), 208KB

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Citation

Sharapov, A. A., & Skvortsov, E. D. (in preparation). Cup product on A-infinity cohomology and deformations.


Cite as: http://hdl.handle.net/21.11116/0000-0003-5497-4
Abstract
We propose a simple method for constructing formal deformations of differential graded algebras in the category of minimal $A_\infty$-algebras. The basis for our approach is provided by the Gerstenhaber algebra structure on the $A_\infty$-cohomology, which we define in terms of the brace operations. As an example, we construct a minimal $A_\infty$-algebra form the Weyl-Moyal $\ast$-product algebra of polynomial functions.