TY - JOUR

T1 - Classification of Simple Lie Superalgebras in Characteristic 2

AU - Bouarroudj, Sofiane

AU - Lebedev, Alexei

AU - Leites, Dimitry

AU - Shchepochkina, Irina

N1 - Funding Information:
This work was partly supported by New York University Abu Dhabi [grant AD 065 to S.B. and D.L.].
Publisher Copyright:
© The Author(s) 2021. Published by Oxford University Press. All rights reserved.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - 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.

AB - 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.

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U2 - 10.1093/imrn/rnab265

DO - 10.1093/imrn/rnab265

M3 - Article

AN - SCOPUS:85152208074

SN - 1073-7928

VL - 2023

SP - 54

EP - 94

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 1

ER -