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

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...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2023-01, Vol.174 (1), p.49-58
Main Authors: FIDELIS, CLAUDEMIR, KOSHLUKOV, PLAMEN
Format: Article
Language:English
Subjects:
Algebra
Lie groups
Polynomials
Rings (mathematics)
Variables
Vector space
Online Access:Get full text
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Summary: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004122000123