Bimodules and branes in deformation quantization
Quantum Algebra
2011-03-31 v4 Mathematical Physics
math.MP
Abstract
We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space . The result implies in particular that the Kontsevich deformation quantizations of and 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.
Keywords
Cite
@article{arxiv.0908.2299,
title = {Bimodules and branes in deformation quantization},
author = {Damien Calaque and Giovanni Felder and Andrea Ferrario and Carlo A. Rossi},
journal= {arXiv preprint arXiv:0908.2299},
year = {2011}
}
Comments
40 pages, 15 figures; a small change of notations in the definition of the 4-colored propagators; an Addendum about the appearance of loops in the $L_\infty$-quasi-isomorphism and a corresponding change in the proof of Theorem 7.2; several changes regarding completions, when dealing with general $A_\infty$-structures