English

L\'evy processes on the Lorentz-Lie algebra

Representation Theory 2021-01-11 v1 Probability

Abstract

L\'evy processes in the sense of Sch\"urmann on the Lie algebra of the Lorentz grouop are studied. It is known that only one of the irreducible unitary representations of the Lorentz group admits a non-trivial one-cocycle. A Sch\"urmann triple is constructed for this cocycle and the properties of the associated L\'evy process are investigated. The decommpositions of the restrictions of this triple to the Lie subalgebras so(3)so(3) and so(2,1)so(2,1) are described.

Keywords

Cite

@article{arxiv.2101.02967,
  title  = {L\'evy processes on the Lorentz-Lie algebra},
  author = {Ameur Dhahri and Uwe Franz},
  journal= {arXiv preprint arXiv:2101.02967},
  year   = {2021}
}

Comments

This work was presented at the "International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics, QP38" held at Tokyo University of Science in October 2017, and has been submitted for publication in the proceedings of that meeting

R2 v1 2026-06-23T21:54:51.092Z