Associative and Jordan Lie Nilpotent Algebras

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-09-19 DOI:10.1007/s10469-024-09755-0

S. V. Pchelintsev

引用次数: 0

Abstract

We look at the interconnection between Lie nilpotent Jordan algebras and Lie nilpotent associative algebras. It is proved that a special Jordan algebra is Lie nilpotent if and only if its associative enveloping algebra is Lie nilpotent. Also it turns out that a Jordan algebra is Lie nilpotent of index 2n + 1 if and only if its algebra of multiplications is Lie nilpotent of index 2n. Finally, we prove a product theorem for Jordan algebras.

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联立和乔丹烈无穷级数

我们研究了李零势约旦代数与李零势关联代数之间的相互联系。研究证明，当且仅当一个特殊的乔丹代数的关联包络代数是 Lie nilpotent 时，它才是 Lie nilpotent 的。此外，当且仅当一个乔丹代数的乘法代数是指数为 2n + 1 的 Lie nilpotent 时，它才是指数为 2n + 1 的 Lie nilpotent。最后，我们证明了乔丹代数的乘积定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.