Automorphism groups of operator algebras

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...

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...

On intertwining operators and finite automorphism groups of vertex operator algebras

Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V G-modules which occur as submodules of irreducible V -modules by using intertwining operators for V . We also determine some fusion rules for a vertex operator algebra as an application.

Operator Algebras, Free Groups and Other Groups

The operator algebras associated to non commutative free groups have received a lot of attention, by F.J. Murray and J. von Neumann and by later workers. We review some properties of these algebras, both for free groups and for other groups such as lattices in Lie groups and Gromov hyperbolic groups. Our guideline is the following list of results for the free group Fn over n ≥ 2 generators. (1)...