LÉVY PROCESSES ON THE LORENTZ-LIE ALGEBRA

Abstract

Levy processes in the sense of Schurmann 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 Schurmann triple is constructed for this cocycle and the properties of the associated Levy process are investigated. The decommpositions of the restrictions of this triple to the Lie subalgebras $so(3)$ and $so(2,1)$ are described.