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Les noyaux de Bergman et Szegö pour des domaines strictment pseudo-convexes qui généralisent la boule.

Jean-Jacques Loeb (1992)

Publicacions Matemàtiques

Let G be a complex semi-simple group with a compact maximal group K and an irreducible holomorphic representation ρ on a finite dimensional space V. There exists on V a K-invariant Hermitian scalar product. Let Ω be the intersection of the unit ball of V with the G-orbit of a dominant vector. Ω is a generalization of the unit ball (case obtained for G = SL(n,C) and ρ the natural representation on Cn).We prove that for such manifolds, the Bergman and Szegö kernels as for the ball are rational fractions...

Lie algebroids and mechanics

Paulette Libermann (1996)

Archivum Mathematicum

We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold M ; the set of units is the zero section identified with the manifold M . We study the Legendre transformation on Lie algebroids.

Lie group extensions associated to projective modules of continuous inverse algebras

Karl-Hermann Neeb (2008)

Archivum Mathematicum

We call a unital locally convex algebra A a continuous inverse algebra if its unit group A × is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group G on a continuous inverse algebra A by automorphisms and any finitely generated projective right A -module E , we construct a Lie group extension G ^ of G by the group GL A ( E ) of automorphisms of the A -module E . This Lie group extension is a “non-commutative” version of the group Aut ( 𝕍 ) of automorphism...

Lie group structures and reproducing kernels on the unit ball of ℂ n

Umberto Sampieri (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si introducono due strutture di gruppo di Lie su un dominio di Siegel omogeneo di ℂ n . Per la palla unitaria si definisce una famiglia ad un parametro di strutture intermedie; ad ognuna di esse viene associato naturalmente un nucleo riproducente ottenendo un'interpolazione tra il nucleo di Bergman ed il nucleo di Szego.

Lie group structures on groups of diffeomorphisms and applications to CR manifolds

M. Salah Baouendi, Linda Preiss Rothschild, Jörg Winkelmann, Dimitri Zaitsev (2004)

Annales de l’institut Fourier

We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.

Lie groupoids of mappings taking values in a Lie groupoid

Habib Amiri, Helge Glöckner, Alexander Schmeding (2020)

Archivum Mathematicum

Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we...

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