Spectral rigidity of group actions: Applications to the case gr

Author:
Oleg N. Ageev

Journal:
Proc. Amer. Math. Soc. **134** (2006), 1331-1338

MSC (2000):
Primary 37A05, 37A15, 37A25, 37A30, 37A35, 28D05, 28D15; Secondary 47A05, 47A35, 47D03

DOI:
https://doi.org/10.1090/S0002-9939-05-08380-2

Published electronically:
October 6, 2005

MathSciNet review:
2199176

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Abstract | References | Similar Articles | Additional Information

Abstract: We apply a technique to study the notion of spectral rigidity of group actions to a group gr. As an application, we prove that there exist rank one weakly mixing transformations conjugate to its square, thereby giving a positive answer to a well-known question.

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Additional Information

**Oleg N. Ageev**

Affiliation:
Department of Mathematics, Moscow State Technical University, 2nd Baumanscaya St. 5, 105005 Moscow, Russia

Address at time of publication:
Max Planck Institute of Mathematics, P.O. Box 7280, D-53072 Bonn, Germany

Email:
ageev@mx.bmstu.ru, ageev@mpim-bonn.mpg.de

DOI:
https://doi.org/10.1090/S0002-9939-05-08380-2

Keywords:
Group actions,
ergodic theory,
conjugations to its squares

Received by editor(s):
November 20, 2004

Published electronically:
October 6, 2005

Additional Notes:
The author was supported in part by the Max Planck Institute of Mathematics, Bonn, and the Programme of Support of Leading Scientific Schools of the RF (grant no. NSh-457.2003.1)

Communicated by:
Michael Handel

Article copyright:
© Copyright 2005
American Mathematical Society