Cubic norm pairs and hermitian cubic norm structures

Abstract: We generalize cubic norm structures to cubic norm pairs and extend hermitian cubic norm structures to arbitrary commutative unital rings. For the associated ``skew dimension one structurable algebra" of these pairs, we construct a corresponding Lie algebra and a group of automorphisms of the Lie algebra. Using the structure of this automorphism group, we also prove that each hermitian cubic norm structure induces an operator Kantor pair.