441 research outputs found
Boundary operator algebras for free uniform tree lattices
Let be a finite connected graph, each of whose vertices has degree at
least three. The fundamental group of is a free group and acts on
the universal covering tree and on its boundary ,
endowed with a natural topology and Borel measure. The crossed product
-algebra depends only on the rank of
and is a Cuntz-Krieger algebra whose structure is explicitly
determined. The crossed product von Neumann algebra does not possess this
rigidity. If is homogeneous of degree then the von Neumann algebra
is the hyperfinite factor of type
where if is bipartite, and
otherwise
Abelian subgroup structure of square complex groups and arithmetic of quaternions
A square complex is a 2-complex formed by gluing squares together. This
article is concerned with the fundamental group of certain square
complexes of nonpositive curvature, related to quaternion algebras. The abelian
subgroup structure of is studied in some detail.Comment: 13 page
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