斜李代数的李导幂的有限生成

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-04-30 DOI:10.1142/s1005386722000177

A. Alahmadi, Fawziah Alharthi

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引用次数: 0

摘要

设[公式:见文本]为特征值不同于2的域上有限生成的关联代数。Herstein问什么时候李代数[公式:见文本]是有限生成的。最近，证明了对于有限生成的零代数[公式:见文]，[公式:见文]的所有派生幂都是有限生成的李代数。设[公式:见文]为有对合的结合代数的偏对称元的李代数。我们考虑李代数[公式:见文]的所有派生幂，并证明了对于任何有对合的有限生成的结合零代数，[公式:见文]的所有派生幂都是有限生成的李代数。

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Finite Generation of Lie Derived Powers of Skew Lie Algebras

Let [Formula: see text] be a finitely generated associative algebra over a field of characteristic different from 2. Herstein asked when the Lie algebra [Formula: see text] is finitely generated. Recently, it was shown that for a finitely generated nil algebra [Formula: see text] all derived powers of [Formula: see text] are finitely generated Lie algebras. Let [Formula: see text] be the Lie algebra of skew-symmetric elements of an associative algebra with involution. We consider all derived powers of the Lie algebra [Formula: see text] and prove that for any finitely generated associative nil algebra with an involution, all derived powers of [Formula: see text] are finitely generated Lie algebras.

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.