Generalized Jordan Polynomials and Bergmann Structions
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 (structions) in the context of Jordan pairs, whose
natural setting is a universal polynomial envelope (with a universal
representation of polynomial operators) generalizing the universal quadratic
envelope (with its universal representation of linear operators). The
Bergmann structions corresponding to fractions are defined only on a subpair
determined by a sesqui-principal inner ideal determined by an element s
and an element n dominated by s. We study these inner ideals and
the criterion for creating structions on them, which will be applied to the
creation of Jordan algebras of fractions. The methods should have future
application to the problem of creating fractions for Jordan pairs.
(This paper is now superseded by the two papers No. 193 and No. 194,
Bergman structions and Generic Jordan polynomials)
K. McCrimmon < kmm4m@virginia.edu >