Abstract
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 ∞-quasi-isomorphic to the deformation quantization of the A ∞-bimodule \(K=\mathbb K\) provided by the Formality Theorem in presence of two branes (Calaque et al., Comput Math 147(01):105–160, 2011).
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Rossi, C.A. The Chevalley–Eilenberg Complex and Deformation Quantization in Presence of Two Branes. Algebr Represent Theor 16, 819–841 (2013). https://doi.org/10.1007/s10468-012-9333-7
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DOI: https://doi.org/10.1007/s10468-012-9333-7