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Lie algebra deformations in characteristic 2PrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2015 (English)In: Mathematical Research Letters, ISSN 1073-2780, Vol. 22, no 2, 353-402 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2015. Vol. 22, no 2, 353-402 p.
##### Keyword [en]

Lie algebra, characteristic 2, Kostrikin-Shafarevich conjecture, Jurman algebra, Kaplansky algebra, deformation
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-117411ISI: 000353051000003OAI: oai:DiVA.org:su-117411DiVA: diva2:814273
#####

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##### Note

Of four types of Kaplansky algebras, type-2 and type-4 algebras have previously unobserved Z/2-gradings: nonlinear in roots. A method assigning a simple Lie superalgebra to every Z/2-graded simple Lie algebra in characteristic 2 is illustrated by seven new series. Type-2 algebras and one of the two type-4 algebras are demystified as nontrivial deforms (the results of deformations) of the alternate Hamiltonian algebras. The type-1 Kaplansky algebra is recognized as the derived of the nonalternate version of the Hamiltonian Lie algebra, the one that preserves a tensorial 2-form. Deforms corresponding to nontrivial cohomology classes can be isomorphic to the initial algebra, e.g., we confirm Grishkov's implicit claim and explicitly describe the Jurman algebra as such a semitrivial deform of the derived of the alternate Hamiltonian Lie algebra. This paper helps to sharpen the formulation of a conjecture describing all simple finite-dimensional Lie algebras over any algebraically closed field of nonzero characteristic and supports a conjecture of Dzhumadildaev and Kostrikin stating that all simple finite-dimensional modular Lie algebras are either of standard type or deforms thereof. In characteristic 2, we give sufficient conditions for the known deformations to be semitrivial.

AuthorCount:4;

Available from: 2015-05-26 Created: 2015-05-19 Last updated: 2015-05-26Bibliographically approvedReferences$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1080",{id:"formSmash:lower:j_idt1080",widgetVar:"widget_formSmash_lower_j_idt1080",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1081_j_idt1083",{id:"formSmash:lower:j_idt1081:j_idt1083",widgetVar:"widget_formSmash_lower_j_idt1081_j_idt1083",target:"formSmash:lower:j_idt1081:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});