The variety of three-dimensional real Jordan algebras (1404.5001v1)

Abstract: In this paper, we study the variety $Jor_{3}$ of three-dimensional Jordan algebras over the field of real numbers. We establish the list of $26$ non-isomorphic Jordan algebras and describe the irreducible components of $Jor_{3}$ proving that it is the union of Zariski closure of the orbits of $8$ rigid algebras.