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

2012/05/31 by Carlo A. Rossi, Rossi, Carlo A.
Mathematics · #17B35 #17B40 #81R60 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #msc:17B35 #msc:17B40 #msc:81R60

paper · pdf · doi:10.48550/arxiv.1205.7029

8 pages, 1 figure; notation changed; corrected many other misprints recently noticed; comments are very welcome!

openalex publication_date 2012/05/31 · arxiv created 2012/10/14 · arxiv updated 2012/10/16 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

For a finite-dimensional Lie algebra \mathfrak g over a field \mathbb K⊃ \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 ⋆ 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).

Citations

• Two-colored noncommutative Gerstenhaber formality and infinity Duflo isomorphism

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