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<p>All the maximal commutative nilpotent subalgebras with nilpotency indices <i>n</i>, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n-2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> in the algebra of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(n\times n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>×</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation> matrices over the field of complex numbers are described up to conjugation. The lengths of the algebras of the first two types were studied previously. In this paper, the lengths of algebras with nilpotency index <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(n-2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> are determined. Bibliography:&#xa0;8 titles.</p>

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LENGTH OF COMMUTATIVE NILPOTENT MATRIX ALGEBRAS WITH LARGE NILPOTENCY INDEX

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • M. A. Khrystik

摘要

All the maximal commutative nilpotent subalgebras with nilpotency indices n, \(n-1\) n - 1 , and \(n-2\) n - 2 in the algebra of \(n\times n\) n × n matrices over the field of complex numbers are described up to conjugation. The lengths of the algebras of the first two types were studied previously. In this paper, the lengths of algebras with nilpotency index \(n-2\) n - 2 are determined. Bibliography: 8 titles.