Hopf algebras and Jordan pairs
by
John R. Faulkner
University of Virginia

Let H be a Z-graded Hopf algebra such that the corresponding Z-grading of the primitive elements has only terms of degrees 1, 0, and -1. Assume that there is a divided power sequence over every primitive element or more generally that there is a homogeneous divided power sequence over every primitive element of degree 1 or -1. A construction from H of a (quadratic) Jordan pair will be given. Also, a new notion of a "representation" of a Jordan pair will be introduced. The universal object for these representations is a Hopf algebra as above. These constructions serve a replacement in all characteristics for the Tits-Kantor-Koecher construction and its reverse which relate Jordan pairs and three term Z-graded Lie algebras in characteristic not two or three. Finally, the Hopf algebra approach allows the introduction of an affine algebraic group for each representation of the Jordan pair.

Date received: February 2, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-63.