Chevalley-Eilenberg复形与双膜形变量子化
The Chevalley--Eilenberg complex and deformation quantization in presence of two branes
摘要：
本文证明了：对于特征为0的域$\mathbb K$上的有限维李代数$\mathfrak g$，若$\mathbb C$包含，则Chevalley-Eilenberg复形$\mathrm U(\mathfrak g)\otimes \wedge(\mathfrak g)$是$\mathrm S(\mathfrak g)$的Koszul复形的变形量子化，是$A_\infty$ -准同构于$A_\infty$的变形量子化，双模$K=\mathbb K$由形式定理提供的存在两个膜（CFFR）。
英文摘要：
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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