Ergodic properties of one-parameter automorphism groups of operator algebras

Examples of one-parameter automorphism groups of UHF algebras

B. Blackadar [1] constructed for the first time an example of a symmetry (or an automorphism of period two) of the CAR algebra (or the UHF algebra of type 2) whose fixed point algebra is not AF (or approximately finite-dimensional). This was soon extended to produce an example of finite-group actions on UHF algebras whose fixed point algebras are not AF [5] and then of compact-group actions [12...

Compact automorphism groups of vertex operator algebras

Let V be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group G of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for G and the irreducible modules for V G which are contained in V where V G is the space of G-invariants of V. We also prove a concomitant Galois correspondence between vertex operator s...

Ergodic Actions of Universal Quantum Groups on Operator Algebras

We construct ergodic actions of compact quantum groups on C∗-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups. In particular, we construct: (1). an ergodic action of the compact quantum Au(Q) on the type IIIλ Powers factor Rλ for an appropriate positive Q ∈ GL(2, R); (2). an ergodic action of the compact...

On Automorphism Groups of C*-algebras

Reflexivity of the Automorphism and Isometry Groups of Some Standard Operator Algebras

In this paper we answer a question raised in [Mol] by giving an example of a proper standard C∗-subalgebra of B(H) whose automorphism and isometry groups are topologically reflexive. After this we prove that in the case of extensions of the C∗-algebra C(H) of all compact operators by separable commutative C∗algebras, these groups are algebraically reflexive. Concerning the most well-known exten...