Sur les semi-caracteres des groupes de Lie resolubles connexes

AbstractLet G be a connected solvable Lie group, π a normal factor representation of G and ψ a nonzero trace on the factor generated by G. We denote by D(G) the space of C∞ functions on G which are compactly supported. We show that there exists an element u of the enveloping algebra UGc of the complexification of the Lie algebra of G for which the linear form ϑ ψ(π(u ∗ ϑ)) on D(G) is a nonzero semiinvariant distribution on G. The proof uses results about characters for connected solvable Lie groups and results about the space of primitive ideals of the enveloping algebra UGc