On the minimal dimension of maximal commutative subalgebras of $M_6(k)$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917436667723776 |
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| author | Nowak-Kępczyk, Małgorzata |
| author_facet | Nowak-Kępczyk, Małgorzata |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23322 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the minimal dimension of maximal commutative subalgebras of $M_6(k)$ Nowak-Kępczyk, Małgorzata Rings and Algebras Commutative Algebra 15A30, 15A27, 16S50, 13H10, 16P10 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. |
| title | On the minimal dimension of maximal commutative subalgebras of $M_6(k)$ |
| topic | Rings and Algebras Commutative Algebra 15A30, 15A27, 16S50, 13H10, 16P10 |
| url | https://arxiv.org/abs/2604.23322 |