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On the Kashiwara–Vergne conjecture

Meinrenken, E.
Published in Inventiones Mathematicae. 2006, vol. 164, no. 3, p. 615 - 634
Collection Open Access - Licence nationale Springer
Abstract Let G be a connected Lie group, with Lie algebra g. In 1977, Duflo constructed a homomorphism of g-modules Duf : S(g) → U(g), which restricts to an algebra isomorphism on invariants. Kashiwara and Vergne (1978) proposed a conjecture on the Campbell-Hausdorff series, which (among other things) extends the Duflo theorem to germs of biinvariant distributions on the Lie group G. The main results of the present paper are as follows. (1) Using a recent result of Torossian (2002), we establish the Kashiwara–Vergne conjecture for any Lie group G. (2) We give a reformulation of the Kashiwara–Vergne property in terms of Lie algebra cohomology. As a direct corollary, one obtains the algebra isomorphism H(g, S(g)) → H(g,U(g)), as well as a more general statement for distributions.
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ALEKSEEV, Anton, MEINRENKEN, E. On the Kashiwara–Vergne conjecture. In: Inventiones Mathematicae, 2006, vol. 164, n° 3, p. 615 - 634. doi: 10.1007/s00222-005-0486-4 https://archive-ouverte.unige.ch/unige:12133

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Deposited on : 2010-10-18

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