Dilation of a class of covariant quantum dynamical semigroups

Kalyan Sinha, Indian Statistical Institute (Delhi Centre)

In a separable C*-algebra with an action of a Lie group on it, the smooth subalgebra with respect to this action can be equipped with a countable family of norms giving it the structure of a Frechet algebra. If the semigroup is covariant, then its (covariant) generator is smooth of some order if and only if the smooth subalgebra is contained in its domain. In analogy with complete boundedness, a natural notion of complete smoothness is introduced and under the additional hypotheses that the generator is completely smooth and that the group is compact, structure maps are constructed on the smooth subalgebra, leading to the associated Evans-Hudson flow - a *-homomorphic quantum stochastic process on the algebra.