Abstract
We give a different proof of the famous result on compatibility between cup product (Kontsevich, 2003, [3, Section 8]) in cohomology of degree 0, for a finite-dimensional Lie algebra, from which we deduce an alternative way of re-writing Kontsevichʼs star product by means of the Alekseev–Torossian connection (Alekseev and Torossian, 2010, [1]).
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