Exactness of one relator groups

Author:
Erik Guentner

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1087-1093

MSC (1991):
Primary 47L85; Secondary 20E06, 22D15

DOI:
https://doi.org/10.1090/S0002-9939-01-06195-0

Published electronically:
October 12, 2001

MathSciNet review:
1873783

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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.

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Additional Information

**Erik Guentner**

Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, Indiana 46202-3216

Address at time of publication:
Mathematical Sciences Research Institute, 100 Centennial Drive, #5070, Berkeley, California 94702-5070

Email:
guentner@msri.org

DOI:
https://doi.org/10.1090/S0002-9939-01-06195-0

Keywords:
Group $C^*$-algebra,
$C^*$-exactness

Received by editor(s):
October 9, 2000

Published electronically:
October 12, 2001

Additional Notes:
The author was supported with funds from the NSF

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2001
American Mathematical Society