NONCOMMUTATIVE MATRIX JORDAN ALGEBRAS

We consider noncommutative degree two Jordan algebras J of two by two matrices whose off diagonal entries are from an anticommutative algebra S. We give generators and relations for the automorphism group of J and determine the derivation algebra Der J in terms of mappings on S. We also give an explicit construction of all S for which Der J does not kill the diagonal idempotents and give conditions for nonisomorphic S's to give isomorphic J 's.