Geometry of generalised Pimsner-Voiculescu extensions

Jacek Brodzki (U Southampton)

Wednesday 2nd May, 2012 16:00-17:00 204


To any subspace of a discrete group one can associate a C*-algebra generated by a contraction of the right regular representation of the group. It is natural to ask for conditions that would imply the existence of a homomorphism from the C*-algebra associated with the subspace to the regular C*-algebra of the group. An answer to this question leads to a geometric construction that associates a C*-algebra extension to a subspace of a discrete group. These extensions generalise the construction of Pimsner and Voiculescu in the case of subspaces of the free group. We will illustrate this construction in a number of cases, including C*-algebra extensions associated with almost-invariant subspaces of groups and amalgamated free products.

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