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Structurable Tori

Bruce Allison·John Faulkner·Yoji Yoshii
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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.

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Bruce Allison, John Faulkner, Yoji Yoshii. 2007-02-22. Structurable Tori. https://arxiv.org/abs/math/0702678

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