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arXiv · 1806.00262

Polynomial identities of the adjoint Lie algebra of $M_{1,1}$

Olga Finogenova·Irina Sviridova
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Abstract

We search an identity basis for the adjoint Lie algebra of the algebra $M_{1,1}(K)$ over a field, where $K$ is either the infinite generated Grassmann algebra $E$ or $E^1$, the variant of the algebra with $1$. In particular, we prove that in the case of an infinite base field of characteristic different from two the identities of $M_{1,1}(E^1)$ are exactly all the consequences of the identity $[x,y,[z,t],v]=0$. We also find an identity basis of $M_{1,1}(E)$ consisting of three identities.

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Olga Finogenova, Irina Sviridova. 2018-06-01. Polynomial identities of the adjoint Lie algebra of $M_{1,1}$. https://arxiv.org/abs/1806.00262

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