Unitary cocycles and processes on the full Fock space
arXiv:1302.2832
Abstract
We consider a unitary cocycle or Schürmann triple on the non-commutative unitary group fixed by a complex matrix which induces an additive free white noise or an additive free Lévy process on the tensor algebra over the full Fock space. A Lévy process on a Voiculescu dual semi-group is given by a generator or Schürmann triple. We will show how a free Lévy process on the non-commutative unitary group fixed by a complex matrix can be obtained by infinitesimally convolving the additive free white noise.
18 pages