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Supercyclic abelian semigroups of matrices on \(\mathbb {C}^{n}\)

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Abstract

We give a complete characterization of a supercyclic abelian semigroup of matrices on \(\mathbb {C}^{n}\). For finitely generated semigroups, this characterization is explicit and it is used to determine the minimal number of matrices in normal form over \(\mathbb {C}\) that form a supercyclic abelian semigroup on \({\mathbb {C}}^{n}\). In particular, no abelian semigroup generated by \(n-1\) matrices on \(\mathbb {C}^{n}\) can be supercyclic.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science of Bizerte, University of Carthage, Jarzouna, 7021, Tunisia

    Habib Marzougui

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  1. Habib Marzougui
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Correspondence to Habib Marzougui.

Additional information

Communicated by J. S. Wilson.

H. Marzougui: Senior Associate of ICTP.

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Marzougui, H. Supercyclic abelian semigroups of matrices on \(\mathbb {C}^{n}\) . Monatsh Math 175, 401–410 (2014). https://doi.org/10.1007/s00605-013-0596-9

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  • DOI: https://doi.org/10.1007/s00605-013-0596-9

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