Lévy processes on the Lorentz-Lie algebra

Ameur Dhahri (1) , Uwe Franz (2)

1 POLIMI - Politecnico di Milano [Milan]
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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 decompositions of the restrictions of this triple to the Lie subalgebras $so(3)$ and $so(2,1)$ are described.

Domaines: Théorie des représentations [math.RT]; Probabilités [math.PR]

Ameur Dhahri, Uwe Franz. Lévy processes on the Lorentz-Lie algebra. International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics, QP38, Noboru Watanabe, Si Si, Oct 2017, Tokyo, Japan. ⟨hal-03103901⟩