Hostname: page-component-6bb9c88b65-x9fsb Total loading time: 0 Render date: 2025-07-25T15:59:31.306Z Has data issue: false hasContentIssue false
  • English
  • Français

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: rafal.pikula@pwr.wroc.pl)
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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