A. Elduque et Jm. Perez, INFINITE-DIMENSIONAL QUADRATIC-FORMS ADMITTING COMPOSITION, Proceedings of the American Mathematical Society, 125(8), 1997, pp. 2207-2216
Composition algebras with a unit element constitute a weil-known class
of algebras. In this paper, those composition algebras with a one-sid
ed unit element are characterized and examples are given of arbitrary
infinite dimension.