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.
gollark: The equipment is mostly capable of both.
gollark: I suppose I could retask the e factories for τ production.
gollark: I wonder if that applies to Gaussian integers. Hmmm. Those aren't ordered → bee, but maybe you can get away without a total ordering here.
gollark: You can do that for reals. It might just be infinitely long.
gollark: No FINITELY undescribable.
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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