Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugation

Details Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugation Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugation

2007-03-12

arxiv.org/abs/math/0703321v2

Journal of Algebra 312 (2007), 668-688

Mathematics

Rings and Algebras

23 pages. Made typographical update in accordance with the final, published version

Scientific paper

10.1016/j.jalgebra.2007.03.007

The exceptional Lie group G_2 acts on the set of real symmetric 7x7-matrices by conjugation. We solve the normal form problem for this group action. In view of earlier results, 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.

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