This analysis identifies lengths of commutative subalgebras in full matrix algebra, suggesting complexity.
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 Mₙ(F). Inspired by [Proposition~4.12]{markova2013}, this paper identifies a class of maximal commutative subalgebras Bk,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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Chengjie Wang (2025) studied this question.
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