On the length of a class of maximal commutative subalgebras

2025/05/14 by Chengjie Wang, Wang, Chengjie
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2505.09268

openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A maximal commutative subalgebra is a substructure in algebra with the greatest commutative property. By studying the lengths of maximal commutative subalgebras, one can more clearly characterize the structure of commutative subalgebras in the full matrix algebra M_n(\mathbbF). Inspired by \cite[Proposition~4.12]markova2013, this paper identifies a class of maximal commutative subalgebras B_k,m,l and computes their lengths. Finally, we present two concrete examples to show that it is not a straightforward generalization.

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