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PROLONGS OF (ORTHO-)ORTHOGONAL LIE (SUPER)ALGEBRAS IN CHARACTERISTIC 2
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 17, 253-309 p.Article in journal (Refereed) Published
Abstract [en]

Cartan described some of the finite dimensional simple Lie algebras and three of the four series of simple infinite dimensional vectorial Lie algebras with polynomial coefficients as prolongs, which now bear his name. The rest of the simple Lie algebras of these two types (finite dimensional and vectorial) are, if the depth of their grading is greater than 1, results of generalized Cartan-Tanaka-Shchepochkina (CTS) prolongs. Here we are looking for new examples of simple finite dimensional modular Lie (super) algebras in characteristic 2 obtained as Cartan prolongs. We consider pairs (an (ortho-)orthogonal Lie (super) algebra or its derived algebra, its irreducible module) and compute the Cartan prolongs of such pairs. The derived algebras of these prolongs are simple Lie (super) algebras. We point out several amazing phenomena in characteristic 2: a supersymmetry of representations of certain Lie algebras, latent or hidden over complex numbers, becomes manifest; the adjoint representation of some simple Lie superalgebras is not irreducible.

Place, publisher, year, edition, pages
2010. Vol. 17, 253-309 p.
Keyword [en]
Modular Lie algebra, modular Lie superalgebra
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URN: urn:nbn:se:su:diva-51233DOI: 10.1142/S1402925110000866ISI: 000284550500012OAI: oai:DiVA.org:su-51233DiVA: diva2:387764
Note
authorCount :3Available from: 2011-01-14 Created: 2011-01-10 Last updated: 2017-12-11Bibliographically approved

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