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arXiv · 1901.04105

Locally nilpotent sets of derivations

Daniel Daigle
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Abstract

Let B be an algebra over a field k and let Der(B) be the set of k-derivations from B to B. We define what it means for a subset of Der(B) to be a locally nilpotent set. We prove some basic results about that notion and explore the following questions. Let L be a Lie subalgebra of Der(B); if every element of L is a locally nilpotent derivation then does it follow that L is a locally nilpotent set? Does it follow that L is a nilpotent Lie algebra?

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Daniel Daigle. 2019-01-14. Locally nilpotent sets of derivations. https://arxiv.org/abs/1901.04105

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