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Mark Grant
Mark Grant
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Let $\mathfrak{g}$ be positively graded Lie algebra over $\mathbb{Q}$, concentrated in even degrees.

Question: If $\mathfrak{g}$ is not free, domust there exist linearly independent elements $a,b\in\mathfrak{g}$ such that $[a,b]=0$?

Let $\mathfrak{g}$ be positively graded Lie algebra over $\mathbb{Q}$, concentrated in even degrees.

Question: If $\mathfrak{g}$ is not free, do there exist linearly independent elements $a,b\in\mathfrak{g}$ such that $[a,b]=0$?

Let $\mathfrak{g}$ be positively graded Lie algebra over $\mathbb{Q}$, concentrated in even degrees.

Question: If $\mathfrak{g}$ is not free, must there exist linearly independent elements $a,b\in\mathfrak{g}$ such that $[a,b]=0$?

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Mark Grant
Mark Grant
  • 35.9k
  • 8
  • 95
  • 198

Zero-divisors in a graded Lie algebra

Let $\mathfrak{g}$ be positively graded Lie algebra over $\mathbb{Q}$, concentrated in even degrees.

Question: If $\mathfrak{g}$ is not free, do there exist linearly independent elements $a,b\in\mathfrak{g}$ such that $[a,b]=0$?