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A 51-dimensional embedding of the Ree–Tits generalized octagon by Kris Coolsaet is a nonfiction available to read on EtoBox.

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We construct an embedding of the Ree-Tits generalized octagon defined over a field K in a 51-dimensional projective space over K arising from a 52-dimensional Lie algebra J of type F 4 . This construction derives from a quadratic map (related to a 'standard' duality of F 4 ) from the 26-dimensional module (see K. Coolsaet, Adv Geometry, to appear) into J. (This embedding is full if and only if K is a perfect field.) We provide explicit formulas for the coordinates of the points of the octagon in this embedding, in terms of their Van Maldeghem coordinates. We apply these results to compute the dimensions of subspaces generated by various special subsets of points of the octagon: the sets of points at a fixed distance from a given point or a given line and the Suzuki suboctagons. The results depend on whether K is the field of 2 elements, or not.

Who reads A 51-dimensional embedding of the Ree–Tits generalized octagon?

Author

Kris Coolsaet

Publisher

Springer; Springer-Verlag; Kluwer Academic Publishers; Springer Science and Business Media LLC; Society for Mining, Metallurgy and Exploration Inc. (ISSN 0925-1022)

Published

2007

Language

EN

Category

nonfiction