Let G be a group generated by a set of affine unipotent transformations T: X → X of the form T(x) = A x + α, where A is a lower triangular unipotent matrix, α 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-2-2,
author = {Rafa\l\ Piku\l a},
title = {On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {133-153},
zbl = {1244.54081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-2-2}
}
Rafał Pikuła. On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus. Studia Mathematica, Tome 196 (2010) pp. 133-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-2-2/