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On the classification of the real flexible division algebras
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
2006 (English)In: Colloquium Mathematicum, ISSN 0010-1354, Vol. 105, no 1, 1-17 p.Article in journal (Refereed) Published
Abstract [en]

We investigate the class of finite-dimensional real flexible division algebras.

We classify the commutative division algebras, completing an approach by Althoen and Kugler. We solve the isomorphism problem for scalar isotopes of quadratic division algebras, and classify the generalised pseudo-octonion algebras. In view of earlier results by Benkart, Britten and Osborn and Cuenca Mira et al., this reduces the problem of classifying the real flexible division algebras to the normal form problem of the action of the group G_2 on the set of positive definite symmetric linear endomorphisms of R^7 by conjugation. A method leading to the solution of this problem is demonstrated.

In addition, the automorphism groups of the real flexible division algebras are described.

Place, publisher, year, edition, pages
2006. Vol. 105, no 1, 1-17 p.
Keyword [en]
Real division algebra, flexible algebra, scalar isotope, generalised pseudo-octonion, group action
National Category
URN: urn:nbn:se:uu:diva-22631OAI: oai:DiVA.org:uu-22631DiVA: diva2:50404
Available from: 2007-01-19 Created: 2007-01-19 Last updated: 2011-01-11

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