2011/04/26 by Ariane Luzia dos Santos, Santos, Ariane Luzia dos, Luiz A. B. San Martín +2
Mathematics · Medicine · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Optimization and Control (math.OC) #math.AT #math.OC
paper · pdf · doi:10.48550/arxiv.1104.5030
18 pages
arxiv created 2011/04/26 · openalex publication_date 2011/04/26 · arxiv updated 2011/04/28 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
Let S be subsemigroup with nonempty interior of a complex simple Lie group G. It is proved that S=G if S contains a subgroup G(α) ≈ Sl(2,ℂ) generated by the exp \mathfrakg± α, where \mathfrakg%α is the root space of the root α. The proof uses the fact, proved before, that the invariant control set of S is contractible in some flag manifold if S is proper, and exploits the fact that several orbits of G(α) are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some improvements.