Guyan Robertson

STRONG SINGULARITY FOR SUBALGEBRAS OF FINITE FACTORS

In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type

Asymptotic

\tto

K

factors arising from countable discrete groups. We give simple criteria for strong singularity, and use them to construct strongly singular subalgebras. We particularly focus on groups which act on geometric objects, where the underlying geometry leads to strong singularity.

-Theory for Groups Acting on

Let

\tA_2

\Gamma

Buildings

be a torsion free lattice in

Negative definite kernels and a dynamical characterization of property (T) for countable groups

G=\PGL(3,{{\mathbb F}})

Irreducible subshifts associated with à 2 buildings

where

Boundary Actions for Affine Buildings and Higher Rank Cuntz-Krieger Algebras

{{\mathbb F}}

BOUNDARY C*-ALGEBRAS FOR ACYLINDRICAL GROUPS

is a nonarchimedean local field. Then