Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugation
Abstract
Description
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.
23 pages. Made typographical update in accordance with the final, published version
23 pages. Made typographical update in accordance with the final, published version