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Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations
Stockholm University, Faculty of Science, Department of Mathematics. New York University Abu Dhabi, United Arab Emirates.
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Number of Authors: 52020 (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.

Place, publisher, year, edition, pages
2020. Vol. 16, article id 089
Keywords [en]
modular vectorial Lie algebra, modular vectorial Lie superalgebra
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-187730DOI: 10.3842/SIGMA.2020.089ISI: 000575380900001OAI: oai:DiVA.org:su-187730DiVA, id: diva2:1510184
Available from: 2020-12-15 Created: 2020-12-15 Last updated: 2024-07-04Bibliographically approved

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Bouarroudj, SofianeLeites, Dimitry

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