Abelian Subalgebras of Von Neumann Algebras from Flat Tori in Locally Symmetric Spaces

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

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

Abelian Subalgebras and the Jordan Structure of a Von Neumann Algebra

For von Neumann algebras M,N not isomorphic to C C and without type I2 summands, we show that for an order-isomorphism f : AbSub M! AbSub N between the posets of abelian von Neumann subalgebras of M and N , there is a unique Jordan ⇤-isomorphism g : M! N with the image g[S] equal to f(S) for each abelian von Neumann subalgebra S of M. The converse also holds. This shows the Jordan structure of ...

Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of Z2-graded Lie algebras

We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial intepretation of these formulas in terms of certain abelian subalgebras of simple Lie algebras.

On the Tensor Products of Maximal Abelian JW-Algebras

It is well known in the work of Kadison and Ringrose 1983 that if A and B are maximal abelian von Neumann subalgebras of von Neumann algebras M and N, respectively, then A⊗B is a maximal abelian von Neumann subalgebra of M⊗N. It is then natural to ask whether a similar result holds in the context of JW-algebras and the JW-tensor product. Guided to some extent by the close relationship between a...