On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus
Studia Mathematica, Tome 201 (2010) no. 2, pp. 133-153
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
group generated set affine unipotent transformations form alpha where lower triangular unipotent matrix alpha constant vector finite dimensional torus enveloping semigroup dynamical system nilpotent group upper lower bounds its nilpotency class obtain description quotient space
Affiliations des auteurs :
Rafa/l Pikuła 1
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title = {On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus},
journal = {Studia Mathematica},
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volume = {201},
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Rafa/l Pikuła. On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus. Studia Mathematica, Tome 201 (2010) no. 2, pp. 133-153. doi: 10.4064/sm201-2-2
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