On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus

Rafał Pikuła. "On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus." Studia Mathematica 201.2 (2010): 133-153. <http://eudml.org/doc/285831>.

@article{RafałPikuła2010,
abstract = {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.},
author = {Rafał Pikuła},
journal = {Studia Mathematica},
keywords = {affine transformation; distal dynamical systems; nilpotent groups; enveloping semigroups},
language = {eng},
number = {2},
pages = {133-153},
title = {On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus},
url = {http://eudml.org/doc/285831},
volume = {201},
year = {2010},
}

TY - JOUR
AU - Rafał Pikuła
TI - On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus
JO - Studia Mathematica
PY - 2010
VL - 201
IS - 2
SP - 133
EP - 153
AB - 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.
LA - eng
KW - affine transformation; distal dynamical systems; nilpotent groups; enveloping semigroups
UR - http://eudml.org/doc/285831
ER -