On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus
Volume 201 / 2010
Studia Mathematica 201 (2010), 133-153
MSC: Primary 54H20; Secondary 37B05.
DOI: 10.4064/sm201-2-2
Abstract
Let $G$ be a group generated by a set of affine unipotent transformations $T:X \to X$ of the form $T(x) = A x + \alpha $, where $A$ is a lower triangular unipotent matrix, $\alpha $ is a constant vector, and $X$ is a finite-dimensional torus. We show that the enveloping semigroup $E(X,G)$ of the dynamical system $(X,G)$ is a nilpotent group and find upper and lower bounds on its nilpotency class. Also, we obtain a description of $E(X,G)$ as a quotient space.
