Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, Indiana 46202-3216
Abstract:
A discrete group is -exact if the reduced crossed product with converts a short exact sequence of --algebras into a short exact sequence of -algebras. A one relator group is a discrete group admitting a presentation where is a countable set and is a single word over . In this short paper we prove that all one relator discrete groups are -exact. Using the Bass-Serre theory we also prove that a countable discrete group acting without inversion on a tree is -exact if the vertex stabilizers of the action are -exact.