On relative property (T) and Haagerup's property
Authors:
Ionut Chifan and Adrian Ioana
Journal:
Trans. Amer. Math. Soc. 363 (2011), 6407-6420
MSC (2010):
Primary 20F69; Secondary 46L10
DOI:
https://doi.org/10.1090/S0002-9947-2011-05259-1
Published electronically:
July 14, 2011
MathSciNet review:
2833560
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Abstract | References | Similar Articles | Additional Information
Abstract: We consider the following three properties for countable discrete groups : (1)
has an infinite subgroup with relative property (T), (2) the group von Neumann algebra
has a diffuse von Neumann subalgebra with relative property (T) and (3)
does not have Haagerup's property. It is clear that (1)
(2)
(3). We prove that both of the converses are false.
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Additional Information
Ionut Chifan
Affiliation:
Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nash- ville, Tennessee 37240 – and – Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Email:
ionut.chifan@vanderbilt.edu
Adrian Ioana
Affiliation:
Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-155505 – and – Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Email:
adiioana@math.ucla.edu
DOI:
https://doi.org/10.1090/S0002-9947-2011-05259-1
Received by editor(s):
July 14, 2009
Received by editor(s) in revised form:
November 23, 2009
Published electronically:
July 14, 2011
Additional Notes:
The second author was supported by a Clay Research Fellowship
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.