Displaying similar documents to “Non linear representations of Lie groups”

On Analytic Vectors for Unitary Representations of Infinite Dimensional Lie Groups

Karl-H. Neeb (2011)

Annales de l’institut Fourier

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Let G be a connected and simply connected Banach–Lie group. On the complex enveloping algebra of its Lie algebra 𝔤 we define the concept of an analytic functional and show that every positive analytic functional λ is integrable in the sense that it is of the form λ ( D ) = 〈 d π ( D ) v , v 〉 for an analytic vector v of a unitary representation of G . On the way to this result we derive criteria for the integrability of * -representations of infinite dimensional Lie algebras of unbounded operators to unitary group...

The Lie group of real analytic diffeomorphisms is not real analytic

Rafael Dahmen, Alexander Schmeding (2015)

Studia Mathematica

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We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense...

Truncated Lie groups and almost Klein models

Georges Giraud, Michel Boyom (2004)

Open Mathematics

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We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M G. Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup.