Related papers: On the Free Jordan Algebras
We determine the isomorphism classes of Jordan algebras in dimension two over the field of real numbers. Using techniques of non-standard analysis we study the properties of the variety of Jordan algebras, and also the contractions among…
I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations…
We define a general notion of partially ordered Jordan algebra (over a partially ordered ring), and we show that the Jordan geometry associated to such a Jordan algebra admits a natural invariant partial cyclic order, whose intervals are…
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan…
There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such…
The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.
In the paper, I consider properties and mappings of free algebra with unit. I consider also conjugation of free algebra with unit.
A special class of Jordan algebras over a field $F$ of characteristic zero is considered. Such an algebra consists of an $r$-dimensional subspace of the vector space of all square matrices of a fixed order $n$ over $F$. It contains the…
Kashuba and Mathieu proposed a conjecture on vanishing of Lie algebra homology, implying a description of the $GL_d$-module structure of the free $d$-generated Jordan algebra. Their conjecture relies on a functorial version of the…
Free extensions of commutative Artinian algebras were introduced by T. Harima and J. Watanabe. The Jordan type of a multiplication map $m$ by a nilpotent element of an Artinian algebra is the partition determining the sizes of the blocks in…
In this short note we prove that every Jordan derivation of triangular algebras is a derivation.
A criterion for elements of free Zinbiel algebras to be Lie or Jordan is established. This criterion is used in studying speciality problems of Tortkara algebras. We construct a base of free special Tortkara algebras. Furthermore, we prove…
We describe the variety of Jordan superalgebras of dimension $4$ whose even part is a Jordan algebra of dimension $1$ or $3$. We prove that the variety is the union of Zariski closures of the orbits of $11$ and $21$ rigid superalgebras,…
A characterization of freeness for plane curves in terms of the Hilbert function of the associated Milnor algebra is given as well as many new examples of rational cuspidal curves which are free. Some stronger properties are stated as…
Quantum theory's Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logic. The reconstruction process is not complete, since it…
We consider cones in a Hilbert space associated to two von Neumann algebras and determine when one algebra is included in the other. If a cone is assocated to a von Neumann algebra, the Jordan structure is naturally recovered from it and we…
We study graded connected algebras over a field of characteristic zero and give an explicit formula for the cyclic homology of a tensor algebra. By means of a slightly new definition of David Anick's notion "strongly free" we are able to…
This note adds to the recent spate of derivations of the probabilistic apparatus of finite-dimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic…
We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.
We introduce and investigate new classes of Jordan algebras which are close to but wider than Rickart and Baer Jordan algebras considered in our previous paper. Such Jordan algebras are called RJ- and BJ-algebras respectively. Criterions…