2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168425The 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.Rings and AlgebrasQuantum Algebra17A30, 17B60, 17A75, 17C40, 17B67text