CORE SYMMETRIES OF A FLOW

For a flow α on a C*-algebra one defines a symmetry as the group of automorphisms γ such that γαγ-1 is a cocycle perturbation of α. We propose to define a core of this symmetry, which acts trivially on the set of equivalence classes of KMS state representations, but may act non-trivially on the set of equivalence classes of covariant irreducible representations. In particular this core acts transitively on the set of those which induce faithful representations of the crossed product by α.

COCYCLE PERTURBATION OF QUASIFREE ALGEBRAIC K-FLOW LEADS TO REQUIRED ASYMPTOTIC DYNAMICS OF ASSOCIATED COMPLETELY POSITIVE SEMIGROUP

We study the quasifree algebraic K-flow τ on the hyperfinite factor ℳ with the expanding subfactor [Formula: see text] generated by representations π of the C*-algebra of the canonical anticommutation relations (CAR) [Formula: see text] over separable Hilbert space ℋ. The type of ℳ and [Formula: see text] can be II1 or IIIλ, 0<λ<1, depending on π. The K-flow τ is obtained by the quasifree lifting of one-parameter group ST consisting of shifts in ℋ with the discrete parameter T=Z or the continuous one T=R. We prove that acting on τ by a quasifree inner Markovian cocycle, one can get the required asymptotic behavior of the perturbed group restriction on [Formula: see text].