Structurable Tori
The classification of structurable tori with nontrivial
involution, which was begun by Allison and Yoshii, is completed. New
examples of structurable tori are obtained using a construction of
structurable algebras from a semilinear version of cubic forms
satisfying the adjoint identity. The classification uses techniques
borrowed from quadratic forms over Z_2 and from the geometry of
generalized quadrangles. Since structurable tori are the coordinate
algebras for the centreless cores of extended affine Lie algebras of
type BC_1, the results of this paper provide a classification and new
examples for this class of Lie algebras.
Bruce Allison < ballison@ualberta.ca >
John Faulkner < jrf@virginia.edu >
Yoji Yoshii < yoji_yoshii@yahoo.co.jp >