Abstract
Let R be a unital *-ring which contains a complex unit and in which the unit can be halved. Conmutativity of R is not assumed. Let Mn and Sn be the Jordan *-triples of the square n×n matrices (respectively, n×n symmetric matrices) (n≥2) with entries in R. The additive groups Der(Mn) and Der(Sn) of the quadratic Jordan derivations of Mn (respectively, Sn) are described in terms of Der(R), the group of quadratic Jordan derivations of R. Particular attention is paid to the case R=C.
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