SPECIALITY OF INTERCONNECTED QUADRATIC JORDAN ALGEBRAS

ABSTRACT

A non-unital quadratic Jordan algebra J with viable n-intercon nectivity () and zero extreme radical is shown to be special. If we assume that J is a simple (non-unital) quadratic Jordan algebra with at least 3 non-zero, non-supplementary orthogonal idempotents, then we show directly (independent from the McCrimmon-Zelmanov classification of simple algebras [7]) that J already is viably 4-interconnected with zero extreme radical, hence is special.

ACKNOWLEDGMENTS

I am greatly indebted to Professor Kevin M. McCrimmon for his time, valuable suggestions, and encouragement.