Primitive Jordan Pairs and Triple Systems

Abstract

In this paper we give a characterization of primitivity of Jordan pairs and triple systems in terms of their local algebras. As a consequence of that local characterization we extend to Jordan pairs and triple systems most of the known results about primitive Jordan algebras. In particular, we describe primitive Jordan pairs and triple systems over an arbitrary ring of scalars in the sense of “The Structure of Primitive Quadratic Jordan Algebras” by J. A. Anquela, T. Cortés, and F. Montaner (1995,J. Algebra172,530–553, 5.1).