Bicontinuity of the Dixmier Map
نویسندگان
چکیده
Let 9 be a solvable Lie algebra over C and let oN be its algebraic adjoint group. The Dixmier map / is a bijective and continuous correspondence between the set 9 * / oN of coadjoint orbits and the set Prim 9 of all the primitive ideals of U(g). Actually the map / (which is the infinitesimal analog of the Kirillov orbits method [K, AK], has been defined by J. Dixmier [Dip Di2], the continuity of / has been proved by N. Berline-Conze, M. Vergne, and M. Duflo [CV, CD], the surjectivity by M. Duflo [Du1, Du2] and the injectivity by R. Rentschler [R, BGR] (Dixmier's book [Di3] contains proofs of all these results). We prove that / is bicontinuous, i.e., that the inverse of / is continuous.
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