I. Jordan algebras in antiquity (1933-1966). I am unable to prove Jordan algebras were known to Archimedes, or that a complete theory has been found in the unpublished papers of Gauss. Their first appearance in recorded history seems to be in the early 1930's when the theory bursts forth full-grown from the mind, not of Zeus, but of Pascual Jordan, John von Neumann, and Eugene Wigner in their 1...

We describe all degenerations of the variety $\mathfrak{Jord}_3$ Jordan algebras dimension three over $\mathbb{C}.$ In particular, we irreducible components in $\mathfrak{Jord}_3.$ For every $n$ define an $n$-dimensional rigid ''marginal'' algebra level one. Also, discuss associative, alternative, left non-commutative Jordan, Leibniz, and anticommutative cases.

In view of this theorem, the study of the structure of commutative algebras with unity element satisfying an identity of degree g 4 is immediately reduced to the study of algebras satisfying one of the identities (l)-(3). The first of these identities is well-known to be equivalent to power-associativity in a commutative algebra of characteristic not 2, 3, or 5 and has been studied extensively ...

In this paper we show that the so-called commutative class of primal-dual interior point algorithms which were designed by Monteiro and Zhang for semidefinite programming extends word-for-word to optimization problems over all symmetric cones. The machinery of Euclidean Jordan algebras is used to carry out this extension. Unlike some non-commutative algorithms such as the XS+SXmethod, this clas...