A note on the Koszul complex in deformation quantization
Quantum Algebra
2011-01-04 v3 Mathematical Physics
math.MP
Abstract
The aim of this short note is to present a proof of the existence of an -quasi-isomorphism between the ---bimodule , introduced in \cite{CFFR}, and the Koszul complex of , viewed as an ---bimodule, for a finite-dimensional (complex or real) vector space.
Cite
@article{arxiv.1002.2561,
title = {A note on the Koszul complex in deformation quantization},
author = {Andrea Ferrario and Carlo A. Rossi and Thomas Willwacher},
journal= {arXiv preprint arXiv:1002.2561},
year = {2011}
}
Comments
8 pages, 1 figure; a more conceptual proof of the existence of an $A_\infty$-bimodule structure on the tensor product of $A_\infty$-bimodules has been added; the proof of Theorem 3.5 has been corrected; some typos have been corrected; acknowledgments modified; added a final remark on the generalization of the result to the framework of \cite{CFFR}