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We study the structure of the generator of a symmetric, conservative quantumdynamical semigroup with norm-bounded generator on a von Neumann algebraequipped with a faithful semifinite trace. For von Neumann algebras withabelian commutant (i.e. type I von Neumann algebras), we give a necessary andsufficient algebraic condition for the generator of such a semigroup to bewritten as a sum of square of self-adjoint derivations of the von Neumannalgebra. This generalizes some of the results obtained by Albeverio,H(phi)egh-Krohn and Olsen [Alb] for the special case of the finite dimensionalmatrix algebras. We also study similar questions for a class of quantumdynamical semigroups with unbounded generators.

A REMARK ON THE STRUCTURE OF SYMMETRIC QUANTUM DYNAMICAL SEMIGROUPS ON VON NEUMANN ALGEBRAS