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arXiv · 0908.2299

Bimodules and branes in deformation quantization

Damien Calaque·Giovanni Felder·Andrea Ferrario·Carlo A. Rossi
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Abstract

We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space $X$. The result implies in particular that the Kontsevich deformation quantizations of $\mathrm{S}(X^*)$ and $\wedge(X)$ associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet's recent paper on Koszul duality in deformation quantization.

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Damien Calaque, Giovanni Felder, Andrea Ferrario, Carlo A. Rossi. 2010-03-04. Bimodules and branes in deformation quantization. https://doi.org/10.1112/s0010437x10004847

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