Abstract
Structurable n-tori are nonassociative algebras with involution that generalize the quantum n-tori with involution that occur as coordinate structures of extended affine Lie algebras. We show that the core of an extended affine Lie algebra of type BC 1 and nullity n is a central extension of the Kantor Lie algebra obtained from a structurable n-torus over C . With this result as motivation, we prove general properties of structurable n-tori and show that they divide naturally into three classes. We classify tori in one of the three classes in general, and we classify tori in the other classes when n=2. It turns out that all structurable 2-tori are obtained from hermitian forms over quantum 2-tori with involution.
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