Lévy Processes on U_q(g) as Infinitely Divisible Representations

1999/07/02 by V. K. Dobrev, H. -D. Doebner, U. Franz +1
Mathematics · #math.PR #msc:60B99 #msc:60G20 #msc:60J30 #msc:17B37 #msc:16W30 #msc:57T05

paper · pdf

published as Contemp. Math. 261 (2000) 181-192 · 13 pages, LATEX file, ASI-TPA/13/99 (TU Clausthal); 6/99 (Preprint-Reihe Mathmatik, Univ. Greifswald);

arxiv created 1999/07/02 · arxiv updated 2009/11/30

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.

Related

• The Theory of Quantum Levy Processes
• q-Levy processes
• Quantum stochastic convolution cocycles II
• Representations of homogeneous quantum Lévy fields
• Quantum stochastic convolution cocycles III