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 centerless cores of extended affine Lie algebras of type BC1, the results of this article provide a classification and new examples for this class of Lie algebras.
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