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Enveloping semigroups of unipotent affine transformations of the torus

Published online by Cambridge University Press:  20 July 2010

RAFAŁ PIKUŁA
RAFAŁ PIKUŁA*
Affiliation:
Department of Mathematics, Ohio State University, 100 Mathematics Building, 231 West 18th Avenue, Columbus, OH 43210-1174, USA (email: [email protected])
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Abstract

We provide a description of the enveloping semigroup of the affine unipotent transformation T:X→X of the form T(x)=Ax+α, where A is a lower triangular unipotent matrix, α is a constant vector, and X is a finite-dimensional torus. In particular, we show that in this case the enveloping semigroup is a nilpotent group whose nilpotency class is at most the dimension of the underlying torus.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 5 , October 2010 , pp. 1543 - 1559
Copyright
Copyright © Cambridge University Press 2009

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References

[1]Ellis, R.. Lectures on Topological Dynamics. W. A. Benjamin, New York, 1969.Google Scholar
[2]Furstenberg, H.. Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton, NJ, 1981.CrossRefGoogle Scholar
[3]Glasner, E.. Minimal nil-transformations of class two. Israel J. Math. 81 (1993), 31–51.CrossRefGoogle Scholar
[4]Milnes, P.. Ellis groups and group extensions. Houston J. Math. 12(1) (1986), 87–108.Google Scholar
[5]Namioka, I.. Ellis groups and compact right topological groups. Contemp. Math. 26 (1984), 295–300.CrossRefGoogle Scholar
[6]Ruppert, W.. Compact Semitopological Semigroups: An Intrinsic Theory. Springer, Berlin, 1984.CrossRefGoogle Scholar