On the compatibility between cup products, the Alekseev--Torossian connection and the Kashiwara--Vergne conjecture


For a finite-dimensional Lie algebra g\mathfrak g over a field KC\mathbb K\supset \mathbb C, we deduce from the compatibility between cup products Kontsevich (2003, Section 8) and from the main result of Shoikhet (2001) an alternative way of re-writing Kontsevich product \star on S(g)\mathrm S(\mathfrak g) by means of the Alekseev--Torossian flat connection (Alekseev and Torossian, 2010). We deduce a similar formula directly from the Kashiwara--Vergne conjecture (Kashiwara and Vergne, 1978).Comment: 8 pages, 1 figure; notation changed; corrected many other misprints recently noticed; comments are very welcome

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