Topological generators of abelian Lie groups and hypercyclic finitely generated abelian semigroups of matrices

Details Topological generators of abelian Lie groups and hypercyclic finitely generated abelian semigroups of matrices Topological generators of abelian Lie groups and hypercyclic finitely generated abelian semigroups of matrices

2011-08-04

arxiv.org/abs/1108.1123v1

Mathematics

Functional Analysis

14 pages

Scientific paper

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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