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Bouarroudj, S., Grozman, P., Lebedev, A., Leites, D. & Shchepochkina, I. (2020). Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations. Symmetry, Integrability and Geometry: Methods and Applications, 16, Article ID 089.
Open this publication in new window or tab >>Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations
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2020 (English)In: Symmetry, Integrability and Geometry: Methods and Applications, E-ISSN 1815-0659, Vol. 16, article id 089Article in journal (Refereed) Published
Abstract [en]

We overview the classifications of simple finite-dimensional modular Lie algebras. In characteristic 2, their list is wider than that in other characteristics; e.g., it contains desuperizations of modular analogs of complex simple vectorial Lie superalgebras. We consider odd parameters of deformations. For all 15 Weisfeiler gradings of the 5 exceptional families, and one Weisfeiler grading for each of 2 serial simple complex Lie superalgebras (with 2 exceptional subseries), we describe their characteristic-2 analogs - new simple Lie algebras. Descriptions of several of these analogs, and of their desuperizations, are far from obvious. One of the exceptional simple vectorial Lie algebras is a previously unknown deform (the result of a deformation) of the characteristic-2 version of the Lie algebra of divergence-free vector fields; this is a new simple Lie algebra with no analogs in characteristics distinct from 2. In characteristic 2, every simple Lie superalgebra can be obtained from a simple Lie algebra by one of the two methods described in arXiv:1407.1695. Most of the simple Lie superalgebras thus obtained from simple Lie algebras we describe here are new.

Keywords
modular vectorial Lie algebra, modular vectorial Lie superalgebra
National Category
Mathematics
Identifiers
urn:nbn:se:su:diva-187730 (URN)10.3842/SIGMA.2020.089 (DOI)000575380900001 ()
Available from: 2020-12-15 Created: 2020-12-15 Last updated: 2024-07-04Bibliographically approved
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-2082-6462

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