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- W2023521690 abstract "Let g be a solvable Lie algebra over C and let _v be its algebraic adjoint group. The Dixmier map I is a bijective and continuous correspondence between the set g* /of coadjoint orbits and the set Prim g of all the primitive ideals of U(g). Actually the map I (which is the infinitesimal analog of the Kirillov orbits method [K, AK], has been defined by J. Dixmier [Dil, Di2j, the continuity of I has been proved by N. Berline-Conze, M. Vergne, and M. Duflo [CV, CD], the surjectivity by M. Duflo [Du,, Du2] and the injectivity by R. Rentschler [R, BGR] (Dixmier's book [Di3] contains proofs of all these results). We prove that I is bicontinuous, i.e., that the inverse of I is continuous." @default.
- W2023521690 created "2016-06-24" @default.
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- W2023521690 date "1991-01-01" @default.
- W2023521690 modified "2023-09-26" @default.
- W2023521690 title "Bicontinuity of the Dixmier map" @default.
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- W2023521690 doi "https://doi.org/10.1090/s0894-0347-1991-1115787-5" @default.
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