2013•Proceedings of the Edinburgh Mathematical SocietyRequires access

Abelian Semigroups of Matrices on ℂnand Hypercyclicity

Adlene Ayadi, Habib Marzougui

Abstract

Abstract We give a complete characterization of a hypercyclic abelian semigroup of matrices on ℂn. For finitely generated semigroups, this characterization is explicit and it is used to determine the minimal number of matrices in normal form over ℂ that form a hypercyclic abelian semigroup on ℂn. In particular, we show that no abelian semigroup generated bynmatrices on ℂncan be hypercyclic.

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Key concepts: Semigroup, Abelian group, Mathematics, Characterization (materials science), Pure mathematics, Cancellative semigroup, Discrete mathematics, Algebra over a field