Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Publication

Dirac Lie Groups, Dirac Homogeneous Spaces and the Theorem of Drinfeld

Madeleine Jotz
2011
Journal Articles

Résumé

The notions of Poisson Lie group and Poisson homogeneous space are extended to the Dirac category. The theorem of Drinfeld on the one-to-one correspondence between Poisson homogeneous spaces of a Poisson Lie group and a special class of Lagrangian subalgebras of the Lie bialgebra associated to the Poisson Lie group is proved to hold in this more general setting.

Source officielle

Madeleine Jotz
2011
Journal Articles

Résumé

Source officielle

Concepts associés (23)

Processus de Poisson

vignette|Schéma expliquant le processus de Poisson Un processus de Poisson, nommé d'après le mathématicien français Siméon Denis Poisson et la loi du même nom, est un processus de comptage classique dont l'équivalent discret est la somme d'un processus de Bernoulli. C'est le plus simple et le plus utilisé des processus modélisant une . C'est un processus de Markov, et même le plus simple des processus de naissance et de mort (ici un processus de naissance pur).

Campbell's theorem (probability)

In probability theory and statistics, Campbell's theorem or the Campbell–Hardy theorem is either a particular equation or set of results relating to the expectation of a function summed over a point process to an integral involving the mean measure of the point process, which allows for the calculation of expected value and variance of the random sum. One version of the theorem, also known as Campbell's formula, entails an integral equation for the aforementioned sum over a general point process, and not necessarily a Poisson point process.

Continuum percolation theory

In mathematics and probability theory, continuum percolation theory is a branch of mathematics that extends discrete percolation theory to continuous space (often Euclidean space Rn). More specifically, the underlying points of discrete percolation form types of lattices whereas the underlying points of continuum percolation are often randomly positioned in some continuous space and form a type of point process. For each point, a random shape is frequently placed on it and the shapes overlap each with other to form clumps or components.

Afficher plus

Publications associées (24)

Afficher plus

Dirac Lie Groups, Dirac Homogeneous Spaces and the Theorem of Drinfeld

Graph Chatbot

Structure-Preserving Reduced Basis Methods For Poisson Systems

Fréchet means in Wasserstein space : theory and algorithms

Gaussian versus Sparse Stochastic Processes : Construction, Regularity, Compressibility