Locally Nilpotent Sets of Derivations

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 319)


Let B be an algebra over a field \(\mathbf {k}\). We define what it means for a subset of \({{\,\mathrm{Der}\,}}_\mathbf {k}(B)\) 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 \({{\,\mathrm{Der}\,}}_\mathbf {k}(B)\); if \(L \subseteq {{\,\mathrm{LND}\,}}(B)\) then does it follow that L is a locally nilpotent set? Does it follow that L is a nilpotent Lie algebra?


Locally nilpotent derivation Nilpotent Lie algebra 

2010 Mathematics Subject Classification

Primary: 14R20 13N15. Secondary: 17B30 17B65 17B66 


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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