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Infinitesimal Generators on the Quantum Group SU_q(2)

Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany

Alternative address: Institut de Recherche Mathématique Avancée, Université de Louis Pasteur Strasbourg, 7, rue René Descartes, F-67084 Strasbourg, France.

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and

Michael Skeide

Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany

Present address: Brandenburgische Technische Universität Cottbus, Postfach 101344, D-03013 Cottbus, Germany.

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https://doi.org/10.1142/S0219025798000314Cited by:8 (Source: Crossref)

Abstract

Quantum Lévy processes on a quantum group are, like classical Lévy processes with values in a Lie group, classified by their infinitesimal generators. We derive a formula for the infinitesimal generators on the quantum group SU_q(2) and decompose them in terms of an infinite-dimensional irreducible representation and of characters. Thus we obtain a quantum Lévy–Khintchine formula.

This work was supported by the Deutsche Forschungsgemeinschaft.