Bimodules and branes in deformation quantization

Details Bimodules and branes in deformation quantization Bimodules and branes in deformation quantization

2009-08-17

arxiv.org/abs/0908.2299v4

Compos.Math.147:105-160,2011

Mathematics

Quantum Algebra

40 pages, 15 figures; a small change of notations in the definition of the 4-colored propagators; an Addendum about the appear

Scientific paper

10.1112/S0010437X10004847

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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