Topological generators of abelian Lie groups and hypercyclic finitely generated abelian semigroups of matrices |
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Authors: | Herbert Abels Antonios Manoussos |
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Institution: | 1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany;2. Fakultät für Mathematik, SFB 701, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany |
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Abstract: | In this paper we bring together results about the density of subsemigroups of abelian Lie groups, the minimal number of topological generators of abelian Lie groups and a result about actions of algebraic groups. We find the minimal number of generators of a finitely generated abelian semigroup or group of matrices with a dense or a somewhere dense orbit by computing the minimal number of generators of a dense subsemigroup (or subgroup) of the connected component of the identity of its Zariski closure. |
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