On the Kashiwara–Vergne conjecture

  title={On the Kashiwara–Vergne conjecture},
  author={A. Alekseev and Eckhard Meinrenken},
  journal={Inventiones mathematicae},
Let G be a connected Lie group, with Lie algebra $\mathfrak{g}$. In 1977, Duflo constructed a homomorphism of $\mathfrak{g}$-modules $\text{Duf}\colon S(\mathfrak{g})\to U(\mathfrak{g})$, 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 bi-invariant distributions on the Lie group G.The main results of the present paper are as follows. (1… 

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