Classification of Simple Lie Superalgebras in Characteristic 2. (30th September 2021)

• Record Type: Journal Article
• Authors: Bouarroudj, Sofiane; Lebedev, Alexei; Leites, Dimitry; Shchepochkina, Irina
• Is Part Of: International mathematics research notices. Volume 2023:Number 1(2023)
• Page Start: 54
• Page End: 94
• Publication Date: 2021-09-30
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnab265
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: 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.