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arXiv · 1812.00403

A proof of Tsygan's formality conjecture for Hamiltonian actions

Chiara Esposito·Niek de Kleijn·Jonas Schnitzer
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Abstract

In this short note we prove an equivariant version of the formality of multidiffirential operators for a proper Lie group action. More precisely, we show that the equivariant Hochschild-Kostant-Rosenberg quasi-isomorphism between the cohomology of the equivariant multidifferential operators and the complex of equivariant multivector fields extends to an $L_\infty$-quasi-isomorphism. We construct this $L_\infty$-quasi-isomorphism using the $G$-invariant formality constructed by Dolgushev. This result has immediate consequences in deformation quantization, since it allows to obtain a quantum moment map from a classical momentum map with respect to a $G$-invariant Poisson structure.

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BibTeXRIS

Chiara Esposito, Niek de Kleijn, Jonas Schnitzer. 2018-12-02. A proof of Tsygan's formality conjecture for Hamiltonian actions. https://arxiv.org/abs/1812.00403

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