The Chevalley--Eilenberg complex and deformation quantization in presence of two branes

Details The Chevalley--Eilenberg complex and deformation quantization in presence of two branes The Chevalley--Eilenberg complex and deformation quantization in presence of two branes

2011-05-30

arxiv.org/abs/1105.5972v2

Mathematics

Quantum Algebra

1 figure; according to remarks of M. Duflo and the anonymous referee, we have added Subsections 4.1, 4.2 and 4.3; we have also

Scientific paper

In this note, we prove that, for a finite-dimensional Lie algebra $\mathfrak g$ over a field $\mathbb K$ of characteristic 0 which contains $\mathbb C$, the Chevalley--Eilenberg complex $\mathrm U(\mathfrak g)\otimes \wedge(\mathfrak g)$, which is in a natural way a deformation quantization of the Koszul complex of $\mathrm S(\mathfrak g)$, is $A_\infty$-quasi-isomorphic to the deformation quantization of the $A_\infty$-bimodule $K=\mathbb K$ provided by the Formality Theorem in presence of two branes (CFFR).

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