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Structure of the Variety of Alternative Algebras with the Lie-Nilpotency Identity of Degree 5
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2024-02-07 , DOI: 10.1134/s0037446624010130 S. V. Pchelintsev
中文翻译:
具有5次李幂零恒等式的多种替代代数的结构
更新日期:2024-02-08
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2024-02-07 , DOI: 10.1134/s0037446624010130 S. V. Pchelintsev
We construct an additive basis for a relatively free alternative algebra of Lie-nilpotent degree 5, describe the associative center and core of this algebra, and find the T-generators of the full center. Also, we give some asymptotic estimate for the codimension of the T-ideal generated by a commutator of degree 5 in a free alternative algebra, and find a finite-dimensional superalgebra that generates the variety of alternative algebras with the Lie-nilpotency of the selfadjoint operator of degree 5.
中文翻译:
具有5次李幂零恒等式的多种替代代数的结构
我们为一个相对自由的李幂零次代数构造了一个加法基,描述了该代数的结合中心和核心,并找到了全中心的T生成元。此外,我们对自由替代代数中 5 次交换子生成的 T 理想的余维数给出了一些渐近估计,并找到了一个有限维超代数,该超代数可生成具有自共轭李零势性的多种替代代数5 级运算符。