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<p>The paper presents a&#xa0;variant of the proof of local finite-dimensionality of Lie PI-algebras with an algebraic adjoint representation over fields of characteristic zero without the use of extremal elements, a&#xa0;number of similar conclusions for such algebras over fields of characteristic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p&gt; 7\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>7</mn> </mrow> </math></EquationSource> </InlineEquation>, and generalizes the description of the locally finite radical of algebraic Mal’tsev locally PI-algebras to any base field of characteristic zero.</p>

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ALGEBRAIC LIE ALGEBRAS WITH FINITE GRADING

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • A. Yu. Golubkov

摘要

The paper presents a variant of the proof of local finite-dimensionality of Lie PI-algebras with an algebraic adjoint representation over fields of characteristic zero without the use of extremal elements, a number of similar conclusions for such algebras over fields of characteristic \(p> 7\) p > 7 , and generalizes the description of the locally finite radical of algebraic Mal’tsev locally PI-algebras to any base field of characteristic zero.