English

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 AA_\infty-quasi-isomorphism between the AA_\infty-S(V)\mathrm S(V^*)-(V)\wedge(V)-bimodule KK, introduced in \cite{CFFR}, and the Koszul complex K(V)\mathrm K(V) of S(V)\mathrm S(V^*), viewed as an AA_\infty-S(V)\mathrm S(V^*)-(V)\wedge(V)-bimodule, for VV 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}

R2 v1 2026-06-21T14:46:28.845Z