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arXiv · 2406.07554

Lie 2-algebras of toral rank 3

Germán Benitez·Carlos R. Payares Guevara·Elkin O. Quintero Vanegas
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Abstract

In this paper we study Lie 2-algebras over an algebraically closed field of characteristic two, which have a triangulable Cartan subalgebra, and derive some general properties of centerless ones. These properties allow us to do an analysis on simple Lie 2-algebras of toral rank three and provide a necessary condition for simplicity. By means of this latter condition we also conclude that simple Lie 2-algebras with a triangulable Cartan subalgebra of toral rank three and of dimension less than or equal to 16 cannot exist.

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Germán Benitez, Carlos R. Payares Guevara, Elkin O. Quintero Vanegas. 2024-03-04. Lie 2-algebras of toral rank 3. https://arxiv.org/abs/2406.07554

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