Jordan Pairs and Hopf Algebras

A (quadratic) Jordan pair is constructed from a -graded Hopf algebra having divided power sequences over all primitive elements and with three terms in the -grading of the primitive elements. The notion of a divided power representation of a Jordan pair is introduced and the universal object is shown to be a suitable Hopf algebra. This serves a replacement for the Tits–Kantor–Koecher construction.