Bruno Vallette - Explicit formulas for the noncommutative Cartan calculus @IhesFr

Uploaded June 2026 | Updated September 2026, 2 weeks ago

The commutative/classical Cartan calculus amonts to a Lie type action of vector fields of a smooth manifold on its de Rham complex of differential forms. Its noncommutative analogue is expected to take the form of a homotopy Lie type action of the Hochschild cochain complex of a (homotopy) associative algebra on its the Hochschild chain complex compatible with Connes' boundary map. Such a structure implies a noncommutative chain-level version of the Gauss-Manin connexion.
In this talk, I will explain how the operadic calculus allows one to solve this problem and I will provide fully explicit formulas in terms of an operad introduced by Kontsevich—Soibelman.

Bruno Vallette (Université Sorbonne Paris-Nord)

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Find this and many more scientific videos on carmin.tv - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.

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Bruno Vallette - Explicit formulas for the noncommutative Cartan calculus

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