相关论文: Structure of associative subalgebras of Jordan ope…

Let g be a simple Lie algebra of rank n over C. We show that the n-dimensional abelian ideals of a Borel subalgebra of g are limits of Jordan Lie subalgebras. Combining this with a classical result by Kostant, we show that the g-module…

Associative or Jordan algebras generated by two idempotents are described precisely.

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…

This paper is devoted to the classification of complex pre-Jordan algebras in the sense of isomorphisms in dimensions $\leq$ 3. All Rota-Baxter operators on complex Jordan algebras in dimensions $\leq$ 3 and the induced pre-Jordan algebras…

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 give an order-theoretic characterization of the essential image of the forgetful functor from the category of real/complex unital C*-algebras to the category of real/complex unital operator systems. It is based on the characterization of…

We consider subalgebras $\mathcal{A}$ of the algebra $M_n$ of $n \times n$ complex matrices that contain all diagonal matrices, known in the literature as the structural matrix algebras (SMAs). Let $\mathcal{A} \subseteq M_n$ be an…

Let $\mathfrak{A}$ and $\mathfrak{B}$ be JBW$^*$-algebras whose sets of unitaries are denoted by $\mathcal{U}(\mathfrak{A})$ and $\mathcal{U}(\mathfrak{B})$, respectively. We show that $\mathcal{U}(\mathfrak{A})$ is closed for Jordan…

The impetus for this study is the work of Dumas and Rigal on the Jordanian deformation of the ring of coordinate functions on $2\times 2$ matrices. We are also motivated by current interest in birational equivalence of noncommutative rings.…

In this paper, we mainly study structure of multiplicative simple Hom-Jordan algebras. We talk about equivalent conditions for multiplicative Hom-Jordan algebras being solvable, simple and semi-simple. As an application, we give a theorem…

We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.

Over a field of characteristic $0$ we give a concrete, computation--ready description of Jordan algebra structures and their low--order deformation theory. The Jordan identity is quartic in the elements and cubic in the multiplication, and…

It is well-known that every algebraic group of type F_4 is the automorphism group of an exceptional Jordan algebra, and that up to isogeny all groups of type ^1E_6 with trivial Tits algebras arise as the isometry groups of norm forms of…

Let $\mathfrak{A}$ and $\mathfrak{A}'$ be two $C^*$-algebras with identities $I_{\mathfrak{A}}$ and $I_{\mathfrak{A}'}$, respectively, and $P_1$ and $P_2 = I_{\mathfrak{A}} - P_1$ nontrivial projections in $\mathfrak{A}$. In this paper we…

In the paper we describe the subcategory of the category of Z-graded Lie algebras which is equivalent to the category of Jordan pairs via a functorial modification of the TKK construction. For instance, we prove that a Z-graded Lie algebra…

This paper is, in a first stage, devoted to establish a topological--algebraic characterization of the principal component, $\mathcal{U}^0 (M)$, of the set of unitary elements, $\mathcal{U} (M)$, in a unital JB$^*$-algebra $M$. We arrive to…

In this note we collect some significant contributions on metric invariants for complex Banach algebras and Jordan--Banach algebras established during the last fifteen years. This note is mainly expository, but it also contains complete…

We investigate surjective isometries between projection lattices of two von Neumann algebras. We show that such a mapping is characterized by means of Jordan $^*$-isomorphisms. In particular, we prove that two von Neumann algebras without…

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…

A Jordan algebra J is said to be pseudo-euclidean if J is endowed with an associative non-degenerate symmetric bilinear form B. B is said an associative scalar product on J. First, we provide a description of the pseudo-euclidean Jordan…