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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An algebraic property of joinings


Authors: Young-Ho Ahn and Mariusz Lemanczyk
Journal: Proc. Amer. Math. Soc. 131 (2003), 1711-1716
MSC (2000): Primary 28D05, 37A05
Published electronically: January 15, 2003
MathSciNet review: 1955257
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Abstract: We show that an ergodic automorphism is semisimple if and only if the set of ergodic self-joinings is a subsemigroup of the semigroup of self-joinings.


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Additional Information

Young-Ho Ahn
Affiliation: Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
Email: ahn@euclid.kaist.ac.kr

Mariusz Lemanczyk
Affiliation: Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18 87-100 Toruń, Poland
Email: mlem@mat.uni.torun.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06893-X
PII: S 0002-9939(03)06893-X
Keywords: Joining, composition of joinings, semisimple, compact extension, relatively independent product, relative weak mixing
Received by editor(s): July 14, 2001
Published electronically: January 15, 2003
Additional Notes: The first author was supported by the KOSEF postdoctoral fellowship program and the Nicholas Copernicus University.
The second author’s research was partly supported by KBN grant P03A 027 21 (2001)
Communicated by: Michael Handel
Article copyright: © Copyright 2003 American Mathematical Society