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New Simple Lie Algebras in Characteristic 2
Stockholm University, Faculty of Science, Department of Mathematics.
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Number of Authors: 5
2016 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, no 18, 5695-5726 p.Article in journal (Refereed) Published
Abstract [en]

Several improvements of the Kostrikin-Shafarevich method conjecturally producing all simple finite-dimensional Lie algebras over algebraically closed fields of any positive characteristic were recently suggested; the list of examples obtained by the improved method becomes richer but in characteristic 2 it is far from being saturated. We investigate one of the steps of our version of the method; in characteristic 2 we describe several new simple Lie algebras and interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. Several new simple Lie superalgebras can be constructed from the newly found simple Lie algebras. We also describe one new simple Lie superalgebra in characteristic 3; it is the only simple Lie superalgebra missed in the approach taken in [6].

Place, publisher, year, edition, pages
2016. no 18, 5695-5726 p.
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URN: urn:nbn:se:su:diva-135091DOI: 10.1093/imrn/rnv327ISI: 000383778900010OAI: diva2:1048776
Available from: 2016-11-22 Created: 2016-10-31 Last updated: 2016-11-22Bibliographically approved

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Leites, Dimitry
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