Regularity action of abelian linear groups on Cⁿ

2011/05/24 by Adlene Ayadi, Ayadi, Adlene, Ezzeddine Salhi +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1105.4686

arxiv created 2011/05/29 · arxiv updated 2011/05/31

Abstract

In this paper, we give a characterization of the action of any abelian subgroup G of GL(n, C) on Cⁿ. We prove that any orbit of G is regular with order m<=2n. Moreover, we give a method to determine this order. In the other hand, we specify the region of all orbits which are isomorphic. If G is finitely generated, this characterization is explicit.

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