Cyclic Compositions and Trisotopies
Cyclic compositions in the sense of Springer and
Knus-Merkurjev-Rost-Tignol are investigated by means of cyclic trisotopies, a
concept originally due to Albert. Using the quadrupling of composition
algebras, we enumerate cyclic trisotopies and compositions in a rational
manner, i.e., without extending the base field. We relate cyclic trisotopies
explicitly to simple associative algebras of degree 3 with involution and to
the Tits process of Albert algebras.
(Updated version 6 Dec 2005)
H. P. Petersson < Holger.Petersson@FernUni-Hagen.de >