Bergman Transformations

The Martinez construction of fractions from a Jordan algebra requires a Jordan derivation involving certain quadratic multiplications on the original algebra. We study a general Bergmann construction of such structural transformations in the context of Jordan pairs. The Bergmann transformations corresponding to fractions are defined only on subpairs determined by sesqui-principal inner ideals, dominions, and we give criterion for a creating structural transformations on them. These results will be applied to the creation of Jordan algebras of fractions, and the methods should have future application to the problem of creating fractions for Jordan pairs.

K. McCrimmon < kmm4m@virginia.edu >