2020/08/27 by Bruno A. Rodrigues, Rodrigues, Bruno A., Luiz A. B. San Martín +3
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2008.12171
openalex publication_date 2020/08/27 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Let \Sl\( n,\ℍ\) be the Lie group of n\× n\nquaternionic matrices g with \vert \det g \vert =1. We prove that\na subsemigroup S \⊂ \Sl\( n,\ℍ\) with nonempty\ninterior is equal to \Sl\( n,\ℍ\) if S contains a\nsubgroup isomorphic to \Sl\( 2,\ℍ\). As application\nwe give sufficient conditions on A,B\∈ mathfraksl\(\nn,\ℍ\) to ensuring that the invariant control system\n\g=Ag+uBg is controllable on \Sl\( n,\ℍ\). We\nprove also that these conditions are generic in the sense that we obtain an\nopen and dense set of controllable pairs \(\nA,B\)\∈ mathfraksl\( n,\ℍ\)2.\n