Structurable Tori
Rings and Algebras
2008-09-06 v1 Quantum Algebra
Abstract
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.
Cite
@article{arxiv.math/0702678,
title = {Structurable Tori},
author = {Bruce Allison and John Faulkner and Yoji Yoshii},
journal= {arXiv preprint arXiv:math/0702678},
year = {2008}
}