Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2020
• ISSN: 1815-0659
• Hauptverfasser: Bouarroudj, Sofiane, Grozman, Pavel, Lebedev, Alexei, Leites, Dimitry, Shchepochkina, Irina
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2020
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/210759
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations. Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites and Irina Shchepochkina. SIGMA 16 (2020), 089, 101 pages

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.