Exponential actions and maximal 𝔇-invariant ideals

Abstract

Let V be an exponential ?-module, ? being an exponential Lie algebra. Put ? = exp ?. Then every orbit of V under the action of ? admits a closed orbit in its closure. If G= exp ? is a nilpotent Lie group and ? an exponential algebra of derivations of ?, then ? = exp ? acts on G, L1(G), (?) and the maximal ?-invariant ideals of L1(G), resp. of (?) coincide with the kernels Ker Ω, resp. Ker Ω∩ (?), where Ω is a closed orbit of ?*.