Cubic norm pairs and hermitian cubic norm structures

Abstract: Cubic norm structures were originally introduced by McCrimmon to generalize Springer's construction of Jordan algebras from a pairing of cubic forms. These cubic norm structures appear naturally in the study of (exceptional) Lie algebras and (exceptional) linear algebraic groups. Later, Allison introduced structurable algebras. One of the main classes of structurable algebras is closely related to cubic norm structures. Moreover, the natural appearances of cubic norm structures can often be understood in terms of this class of structurable algebras. To better understand this class of structurable algebras, De Medts introduced hermitian cubic norm structures. In this talk, we introduce cubic norm pairs and hermitian cubic norm structures over arbitrary commutative rings and construct an associated structurable algebra, Lie algebra, and automorphism group. We also study the behaviour of certain automorphism groups.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar