On projective embeddings of partial planes and rank three matroids
by Franz B. Kalhoff
Abstract:
Abstract. Any finite partial plane I, and thus any finite linear space and any
(simple) rank three matroid, can be embedded into a translation plane. It even
turns out, that I is embeddable into a projective plane of Lenz class V, and that
the characteristic of this plane can be chosen arbitrarily. In particular, any
rank three matroid is realizable over a (not necessarily associative) division
algebra.
Key words and phrases:
Rank 3 matroids, linear spaces, partial planes, projective
embeddings, finite projective planes, translation planes, Lenz-Barlotti
classification, (non associative) division algebras.
1991 Mathematics Subject Classification: Primary 05 B 35; Secondary 51 A 54, 17 A 35 (05 B 25, 51 E 14, 51 A 35).
Published in: Discrete Math. 163 (1997), 67 - 79.
Contact: Franz.Kalhoff@Mathematik.Uni-Dortmund.DE