Lévy Processes on $U_q(g)$ as Infinitely Divisible Representations

Abstract

Lévy processes on bialgebras are families of infinitely divisible representations. We classify the generators of Lévy processes on the compact forms of the quantum algebras $U_q(g)$, where $g$ is a simple Lie algebra. Then we show how the processes themselves can be reconstructed from their generators and study several classical stochastic processes that can be associated to these processes.

13 pages, LATEX file, ASI-TPA/13/99 (TU Clausthal); 6/99 (Preprint-Reihe Mathmatik, Univ. Greifswald);