Inner product modules arising from compact automorphism groups of von Neumann 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...

Von Neumann Algebras Arising from Bost-connes Type Systems

The Bost-Connes system [4] is a C∗-dynamical system such that for inverse temperatures β > 1 the extremal KMSβ-states carry a free transitive action of the Galois group of the maximal abelian extension of Q, have type I and partition function ζ(β), while for every β ∈ (0, 1] there exists a unique KMSβ-state of type III1. The uniqueness and the type of the KMSβ-states in the critical interval (0...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Involutions on Algebras Arising from Locally Compact Groups Paul

Two Banach algebras are naturally associated with a locally compact group G: the group algebra, L,(G), and the measure algebra, M(G). For these two Banach algebras we determine all isometric involutions. Each of these Banach algebras has a natural involution. We will show that an isometric involution, (*), is the natural involution on £'(<?) if and only if the closure in the strict topology of ...

Relative Tensor Products for Modules over von Neumann Algebras

We give an overview of relative tensor products (RTPs) for von Neumann algebra modules. For background, we start with the categorical definition and go on to examine its algebraic formulation, which is applied to Morita equivalence and index. Then we consider the analytic construction, with particular emphasis on explaining why the RTP is not generally defined for every pair of vectors. We also...