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Zero-divisors in a graded Lie algebra

Consider the complex Lie algebra $\mathfrak{h}=\mathbb{C}[t,t^{-1}]\partial_t$ with Lie bracket $$[t^m\partial_t,t^n\partial_t]=(n-m)t^{n+m-1}\partial_t$$ ie the natural bracket that arises considerin …
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