Sur les semi-caracteres des groupes de Lie resolubles connexes |
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Authors: | Jean-Yves Charbonnel |
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Institution: | UER de Maths, Université Paris VII, couloir 45-55, 5 ° étage, 2 Place Jussieu 75005, Paris, France |
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Abstract: | Let 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 (G) the space of C∞ functions on G which are compactly supported. We show that there exists an element u of the enveloping algebra U of the complexification of the Lie algebra of G for which the linear form on (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 U. |
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