Duflo isomorphism

In mathematics, the Duflo isomorphism is an isomorphism between the center of the universal enveloping algebra of a finite-dimensional Lie algebra and the invariants of its symmetric algebra. It was introduced by Michel Duflo (1977).

The isomorphism also follows from the Kontsevich formality theorem.

Properties

For a nilpotent Lie algebra the Duflo isomorphism coincides with the symmetrization map from symmetric algebra to universal enveloping algebra. For a semisimple Lie algebra the Duflo isomorphism is compatible in a natural way with the Harish-Chandra isomorphism.

References

Duflo, Michel (1977), "Opérateurs différentiels bi-invariants sur un groupe de Lie", Annales Scientifiques de l'École Normale Supérieure, Série 4, 10 (2): 265–288, ISSN 0012-9593, MR 0444841
Calaque, Damien; Rossi, Carlo A. (2011), Lectures on Duflo isomorphisms in Lie algebra and complex geometry (PDF), EMS Series of Lectures in Mathematics, Zürich: European Mathematical Society, ISBN 978-3-03719-096-8, MR 2816610

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