Groupoid normalisers of tensor products: infinite von Neumann algebras

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...

Quasicrystals, aperiodic order, and groupoid von Neumann algebras

Vanishing of the Cyclic Cohomology of Infinite Von Neumann Algebras

We prove that if A is an infinite von Neumann algebra (i. e., the identity can be decomposed as a sum of a sequence of pairwise disjoint projections, all equivalent to the identity) then the cyclic cohomology of A vanishes. We show that the method of the proof applies to certain algebras of infinite matrices.

Vanishing of Second Cohomology for Tensor Products of Type Ii1 Von Neumann Algebras

We show that the second cohomology group H2(M⊗N, M⊗N) is always zero for arbitrary type II1 von Neumann algebras M and N .

Compressions of Free Products of Von Neumann Algebras

A reduction formula for compressions of von Neumann algebra II1–factors arising as free products is proved. This shows that the fundamental group is R + for some such algebras. Additionally, by taking a sort of free product with an unbounded semicircular element, continuous one parameter groups of trace scaling automorphisms on II∞–factors are constructed; this produces type III1 factors with c...