Associative and Jordan Lie Nilpotent Algebras

被引：0
|
作者：
Pchelintsev, S. V. [1 ,2 ,3 ]
机构：
[1] St Petersburg State Univ, St Petersburg, Russia
[2] Finance Acad Govt Russian Federat, Moscow, Russia
[3] Moscow City Teachers Training Univ, Moscow, Russia
来源：
ALGEBRA AND LOGIC | 2024年
基金：
俄罗斯科学基金会;
关键词：
associative algebra; Jordan algebra; Lie nilpotent algebra; product theorem for Jordan algebras; IDEALS;
D O I：
10.1007/s10469-024-09755-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页数：17
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