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

2011/08/04 by Herbert Abels, Abels, Herbert, Antonios Manoussos +1
Mathematics · #20F05 #22E10 #22E15 #37C85 #47A16 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47D03 #Secondary 20G20 #math.FA #msc:20F05 #msc:20G20 #msc:22E10 #msc:22E15 #msc:37C85 #msc:47A16 #msc:47D03

paper · pdf · doi:10.48550/arxiv.1108.1123

14 pages

arxiv created 2011/08/04 · arxiv updated 2011/08/05

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.

Related

• A method to find generators of a semi-simple Lie group via the topology of its flag manifolds
• Hypercyclic abelian semigroups of affine maps on Cⁿ
• Large sets of generating tuples for Lie groups
• Hypercyclic Abelian Affine Groups
• Semigroups of matrices with dense orbits