On small matrix subalgebras with a trivial centralizer |
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| Authors: | Clément de Seguins Pazzis |
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| Institution: | 1. Lycée Privé Sainte-Geneviève , 2, rue de l'école des Postes, 78029 Versailles Cedex, France dsp.prof@gmail.com |
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| Abstract: | Given an integer n?≥?3, we investigate the minimal dimension of a subalgebra of M n (𝕂) with a trivial centralizer. It is shown that this dimension is 5 when n is even and 4 when it is odd. In the latter case, we also determine all 4-dimensional subalgebras with a trivial centralizer. |
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| Keywords: | commutation matrices algebras dimension centralizer |
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