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New simple Lie superalgebras in characteristic 3

Alberto Elduque
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Abstract

Symplectic (respectively orthogonal) triple systems provide constructions of Lie algebras (resp. superalgebras). However, in characteristic 3, it is shown that this role can be interchanged and that Lie superalgebras (resp. algebras) can be built out of symplectic triple systems (resp. orthogonal triple systems) with a different construction. As a consequence, new simple finite dimensional Lie superalgebras, as well as new models of some nonclassical simple Lie algebras, are obtained over fields of characteristic 3.

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Alberto Elduque. 2004-12-20. New simple Lie superalgebras in characteristic 3. https://arxiv.org/abs/math/0412395

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