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arXiv · 1205.7029

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

Carlo A. Rossi
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Abstract

For a finite-dimensional Lie algebra $\mathfrak g$ over a field $\mathbb K\supset \mathbb C$, 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 $\mathrm S(\mathfrak g)$ 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).

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Carlo A. Rossi. 2012-10-14. On the compatibility between cup products, the Alekseev--Torossian connection and the Kashiwara--Vergne conjecture. https://arxiv.org/abs/1205.7029

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