Classification of Simple Lie Superalgebras in Characteristic 2

Sofiane Bouarroudj, Alexei Lebedev, Dimitry Leites, Irina Shchepochkina

Research output: Contribution to journalArticlepeer-review


All results concern characteristic 2. We describe two procedures; each of which to every simple Lie algebra assigns a simple Lie superalgebra. We prove that every simple finite-dimensional Lie superalgebra is obtained as the result of one of these procedures. For Lie algebras, in addition to the known “classical” restrictedness, we introduce a (2,4)-structure on the two non-alternating series: orthogonal and Hamiltonian vector fields. For Lie superalgebras, the classical restrictedness of Lie algebras has two analogs: a 2|4-structure, which is a direct analog of the classical restrictedness, and a novel 2|2-structure-one more analog, a (2, 4)|4-structure on Lie superalgebras is the analog of (2,4)-structure on Lie algebras known only for non-alternating orthogonal and Hamiltonian series.

Original languageEnglish (US)
Pages (from-to)54-94
Number of pages41
JournalInternational Mathematics Research Notices
Issue number1
StatePublished - Jan 1 2023

ASJC Scopus subject areas

  • General Mathematics


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