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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: rafal.pikula@pwr.wroc.pl)
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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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