Octonion algebras over schemes and the equivalence of isotopes and isometric forms

Abstract: In 2019, Alsaody and Gille show that, for octonion algebras over unital commutative rings, there is an equivalence between isotopes and isometric quadratic forms. This leads us to a question: can this equivalence be generalized to octonion algebras over a (not necessarily affine) scheme? We give the basic definitions of octonion algebras over schemes. We show that an isotope of an octonion algebra C over a scheme is isomorphic to a twist by an Aut(C)–torsor. We conclude by giving an affirmative answer to our question.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar