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 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, European Mathematical Society (EMS), Zürich, ISBN 978-3-03719-096-8, MR 2816610