Abstract
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 ≠ 2 by Racine and Zelmanov. Here, we determine the centroids of the analog of these superalgebras over general rings of scalars and show that they have no odd centroid, suggesting that ordinary scalars are the proper concept.
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