Jordan pairs and Hopf algebras

A (quadratic) Jordan pair is constructed from a Z-graded Hopf algebra havin g divided power sequences over all primitive elements and with three terms in the Z-grading of the primitive elements. The notion of a divided power r epresentation of a Jordan pair is introduced and the universal object is sh own to be a suitable Hopf algebra. This serves a replacement for the Tits-K antor-Koecher construction. (C) 2000 Academic Press.