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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Published in:Mathematical proceedings of the Cambridge Philosophical Society 2023-01, Vol.174 (1), p.49-58
Main Authors: FIDELIS, CLAUDEMIR, KOSHLUKOV, PLAMEN
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Language:English
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Algebra
Lie groups
Polynomials
Rings (mathematics)
Variables
Vector space
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description 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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subjects Algebra
Lie groups
Polynomials
Rings (mathematics)
Variables
Vector space
title mathbb{Z}$ -graded identities of the Lie algebras $U_1$ in characteristic 2
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