Summary: Department of Mathematics & Statistics
GRADUATE STUDENT SEMINAR1
Speaker: Hongyun Dong
Title: Boundaries of reduced free group C -algebras
Date: Friday, April 25, 2008
Time: 1.30 pm
Location: Classroom Building 251
A C -dynamical system .A; G; / is a triple consisting of a C -algebra A, a locally
compact group G and a homomorphism of G into the automorphism group Aut(A) of
A. We denote the automorphism for s in G by s. The crossed product is a C -algebra
built out of a dynamical system. Similar to group C -algebras, when the group G is
amenable, the reduced crossed product equals the full crossed product.
This crossed product has the universal property: if . ; U / is any covariant representa-
tion of .A; G; /, then there is representation of A G into C . .A/; U.G//.
Let denote the free group of rank 2 Ä r Ä 1. From the last seminar I gave, we
know that is not amenable. However, is hyperbolic and the action of a hyperbolic
group on its boundary is amenable. Also Cr ./ is exact.
.@; / be the crossed product von Neumann algebra, where @ is the