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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 algebra structure in the model of 3-link snake robot

Martin Doležal (2024)

Archivum Mathematicum

In this paper, we study a 5 dimensional configuration space of a 3-link snake robot model moving in a plane. We will derive two vector fields generating a distribution which represents a space of the robot’s allowable movement directions. An arbitrary choice of such generators generates the entire tangent space of the configuration space, i.e. the distribution is bracket-generating, but our choice additionally generates a finite dimensional Lie algebra over real numbers. This allows us to extend...

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 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 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.

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