uu.seUppsala University Publications

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Normal forms for the G2-action on the real symmetric 7 × 7-matrices by conjugationPrimeFaces.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}); 2007 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 312, no 2, p. 668-688Article in journal (Refereed) Published
##### Abstract [en]

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

2007. Vol. 312, no 2, p. 668-688
##### Keyword [en]

Normal form, Group action, Vector product, Octonion, Automorphism, Real division algebra, Flexible algebra
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-97995DOI: 10.1016/j.jalgebra.2007.03.007ISI: 000247409100009OAI: oai:DiVA.org:uu-97995DiVA, id: diva2:173145
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Available from: 2009-01-29 Created: 2009-01-29 Last updated: 2017-12-14Bibliographically approved
##### In thesis

The exceptional Lie group G(2) subset of O-7 (R) acts on the set of real symmetric 7 x 7-matrices by conjugation. We solve the normal form problem for this group action. In view of the earlier results [G.M. Benkart, D.J. Britten, J.M. Osbom, Real flexible division algebras, Canad. J. Math. 34 (1982) 550-588; J.A. Cuenca Mira, R. De Los Santos Villodres, A. Kaidi, A. Rochdi, Real quadratic flexible division algebras, Linear Algebra Appl. 290 (1999) 1-22; E. Darpb, On the classification of the real flexible division algebras, Colloq. Math. 105 (1) (2006) 1-17], this gives rise to a classification of all finite-dimensional real flexible division algebras. By a classification is meant a list of pairwise non-isomorphic algebras, exhausting all isomorphism classes. We also give a parametrisation of the set of all real symmetric matrices, based on eigen values.

1. Problems in the Classification Theory of Non-Associative Simple Algebras$(function(){PrimeFaces.cw("OverlayPanel","overlay173149",{id:"formSmash:j_idt892:0:j_idt899",widgetVar:"overlay173149",target:"formSmash:j_idt892:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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