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Normal forms for the G2-action on the real symmetric 7 × 7-matrices by conjugation
Uppsala universitet.ORCID iD: 0000-0001-9177-9774
2007 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 312, 668-688 p.Article in journal (Refereed) Published
Abstract [en]

The exceptional Lie group G2 ⊂ O7 (R) acts on the set of real symmetric 7 × 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. Osborn, 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. Darpö, 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 eigenvalues.

Place, publisher, year, edition, pages
2007. Vol. 312, 668-688 p.
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-21726DOI: 10.1016/j.jalgebra.2007.03.007OAI: oai:DiVA.org:mdh-21726DiVA: diva2:652506
Available from: 2013-09-30 Created: 2013-09-30 Last updated: 2014-12-08Bibliographically approved

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Publisher's full texthttp://dx.doi.org/10.1016/j.jalgebra.2007.03.007

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