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$\mathbb{Z}$-graded identities of the Lie algebras $U_1$ in characteristic 2
Published online by Cambridge University Press: 08 March 2022
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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 174 , Issue 1 , January 2023 , pp. 49 - 58
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society
Footnotes
Supported by FAPESP grant No. 2019/12498-0.
Partially supported by FAPESP grant No. 2018/23690-6 and by CNPq grant No. 302238/2019-0.
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