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arXiv · 2604.23322

On the minimal dimension of maximal commutative subalgebras of $M_6(k)$

Małgorzata Nowak-Kępczyk
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Abstract

We study the minimal dimension of maximal commutative subalgebras of the matrix algebra $M_n(k)$ over an algebraically closed field. While examples with dimension strictly smaller than n are known for $n \geq 14$, no such examples are known in smaller dimensions. In this paper, we show that for n = 6 every maximal commutative subalgebra $A\subset M_6(k)$ satisfies $\dim A \geq 6$. The proof is based on a detailed analysis of local algebras and their module structure, combined with explicit estimates of the dimension of the centralizer.

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Małgorzata Nowak-Kępczyk. 2026-04-25. On the minimal dimension of maximal commutative subalgebras of $M_6(k)$. https://arxiv.org/abs/2604.23322

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