A note on the Koszul complex in deformation quantization

Details A note on the Koszul complex in deformation quantization A note on the Koszul complex in deformation quantization

2010-02-12

arxiv.org/abs/1002.2561v3

Lett.Math.Phys.95:27-39,2011

Mathematics

Quantum Algebra

8 pages, 1 figure; a more conceptual proof of the existence of an $A_\infty$-bimodule structure on the tensor product of $A_\i

Scientific paper

10.1007/s11005-010-0439-8

The aim of this short note is to present a proof of the existence of an $A_\infty$-quasi-isomorphism between the $A_\infty$-$\mathrm S(V^*)$-$\wedge(V)$-bimodule $K$, introduced in \cite{CFFR}, and the Koszul complex $\mathrm K(V)$ of $\mathrm S(V^*)$, viewed as an $A_\infty$-$\mathrm S(V^*)$-$\wedge(V)$-bimodule, for $V$ a finite-dimensional (complex or real) vector space.

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