Length of commutative nilpotent matrix algebras with large nilpotency index

M. A. Khrystik<sup>ab

a</sup> National Research University Higher School of Economics, Moscow
^b Moscow Center for Fundamental and Applied Mathematics

Abstract: The monograph by D. A. Suprunenko and R. I. Tyshkevich on commutative matrix algebras describes, up to conjugation, all maximal commutative nilpotent subalgebras of nilpotency indices $n$, $n-1$, and $n-2$ in the algebra of matrices of order $n$ over the field of complex numbers. The lengths of the algebras of the first two types were investigated by O. V. Markova. In this paper, the lengths of all algebras of the third type are computed.

Key words and phrases: matrix algebras, length of an algebra, nilpotent algebras.

UDC: 512.643

Received: 01.10.2025