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 >