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arXiv · 2112.15048

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

Claudemir Fidelis·Plamen Koshlukov
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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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Claudemir Fidelis, Plamen Koshlukov. 2021-12-30. $\mathbb{Z}$-graded identities of the Lie algebras $U_1$ in characteristic 2. https://doi.org/10.1017/s0305004122000123

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