Sur l'inverse de l'application de Dixmier pour une algèbre de Lie résoluble

✍ Scribed by Jean-Yves Charbonnel

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 292 KB
• Volume: 226
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8152

✦ Synopsis

Let be a completely solvable Lie algebra over a field of characteristic zero. Let  be the algebra of differential operators with formal power series coefficients. The subalgebra generated by the Weyl algebra A on and the formal power series with rational coefficients in the weights of the adjoint representation is denoted by P . There is a canonical imbedding L of the enveloping algebra U in P . For every derivation x of , the adjoint vector field on defined by -x is denoted by W x . Let a be the biggest nilpotent ideal in the algebraic hull of the image of by the adjoint representation. For every prime ideal I in U , let M I be the quotient of P by the left ideal generated by L I and W a . The main result connects β I and M I where β I is the inverse image of the Dixmier map for . To state this result, certain categories Mod J P are introduced and β I is described in terms of the set of all J such that M I is in Mod J P .