On the structure of covariant dynamical semigroups (Q1897275)

The author studies dynamical semigroups in \({\mathfrak B} ({\mathcal H})\) without the norm-continuity assumption by introducing the notion of a form- generator, giving the mathematical expression for the idea of Markovian master equation. He shows that any form-generator on \({\mathfrak B} ({\mathcal H})\) admits a standard representation, and describes the non-uniqueness of this representation. The equations for the components of the standard representation of a covariant form-generator are deduced in terms of low- order cohomology of the symmetry group; in particular he obtains noncommutative Levy-Khinchin-type formulae for the shift-covariant form- generators. Relations with previous works on characterization of the (unbounded) generator of a dynamical semigroup are discussed.