Structurable tori and extended affine Lie algebras of type BC1

Structurablen-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 BC1 and nullity n is a central extension of the Kantor Lie algebra obtained from a structurablen-torus over . With this result as motivation, we prove general properties of structurablen-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.