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Nilpotent Lie groups: Fourier inversion and prime ideals

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OAS - Operator algebras: subfactors and their applications

In this talk, I will give a version of the Fourier inversion theorem for connected, simply connected nilpotent Lie groups G = exp(g) by showing that there is a continuous retract from the space of adapted smooth kernel functions defined on a sub-manifold of g* into the Schwartz functions defined on G.  As an application, I will give a characterisation of a class of invariant prime ideals of L1(G).




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