Year: 2007
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Allison, Bruce, Faulkner, John, Yoshii, Yoji
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394671771