李代数$U_1$在特征2上的$\mathbb{Z}$ -阶恒等式

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2021-07-22 DOI:10.1017/S0305004122000123

Claudemir Fidelis, P. Koshlukov

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引用次数: 1

摘要

摘要:设K为特征二的任意域，设$U_1$和$W_1$分别为洛朗多项式$K[t,t^{-1}]$和多项式环K[t] $的导数的李代数。代数$U_1$和$W_1$具有自然的$\mathbb{Z}$ -分级。本文给出了$U_1$和$W_1$的梯度恒等式的基，并证明了它们不存在任何有限基。

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$\mathbb{Z}$ -graded identities of the Lie algebras $U_1$ in characteristic 2

Abstract Let K be any field of characteristic two and let $U_1$ and $W_1$ be the Lie algebras of the derivations of the algebra of Laurent polynomials $K[t,t^{-1}]$ and of the polynomial ring K[t], respectively. The algebras $U_1$ and $W_1$ are equipped with natural $\mathbb{Z}$ -gradings. In this paper, we provide bases for the graded identities of $U_1$ and $W_1$ , and we prove that they do not admit any finite basis.

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来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.