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arXiv · 2608.13379

Simple double Lie algebras on the Laurent polynomial space

Vsevolod Gubarev
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Abstract

We construct a simple $\lambda$-double Lie algebra on $k[t,t^{-1}]$ for every nonzero $\lambda\in k$. We then show that the analogous two-sided construction of weight zero is also simple. Both products admit natural coefficient realizations via row-and-column-finite operators associated with the finitary $\mathbb Z\times\mathbb Z$ matrix algebra.

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Vsevolod Gubarev. 2026-08-13. Simple double Lie algebras on the Laurent polynomial space. https://arxiv.org/abs/2608.13379

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