Centroids of Quadratic Jordan Superalgebras
The centroid of a Jordan superalgebra consists
of the natural ``superscalar multiplications'' on the superalgebra.
A philosophical question is whether the natural concept of
``scalar'' in the category of superalgebras should be that of
superscalars or ordinary scalars. Basic examples of Jordan
superalgebras are the simple Jordan superalgebras with semisimple
even part, which were classified over an algebraically closed field
of characteristic not 2 by M. Racine and E. Zelmanov. Here, we
determine the centroids of the analogues of these superalgebras over
general rings of scalars and show that they have no odd centroid,
suggesting that ordinary scalars are the proper concept.
(Updated version 5 August 2006)
Pamela A. Richardson < richarpa@westminster.edu >