Related papers: Jordan quadruple systems
In 2003 Peter Cameron introduced the concept of a Jordan scheme and asked whether there exist Jordan schemes which are not symmetrisations of coherent configurations (proper Jordan schemes). The question was answered affirmatively by the…
Let $\mathbb{K}$ be a field of characteristic different from $2$, and let $M_n(\mathbb{K})$ be the algebra of all $n\times n$ matrices over $\mathbb{K}$. We consider the corresponding special Jordan algebra $\mathcal{A}:=M_n(\mathbb{K})^+$…
We introduce some basic notions and results for quaternionic linear operators analogous to those for complex linear operators. Our main result is to prove the additive and multiplicative Jordan-Chevalley decompositions for quaternionic…
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…
In this article we begin the study of representations of simple finite-dimensional noncommutative Jordan superalgebras. In the case of degree $\geq 3$ we show that any finite-dimensional representation is completely reducible and, depending…
In this paper we describe all subalgebras and automorphisms of simple noncommutative Jordan superalgebras $K_3(\alpha,\beta,\gamma)$ and $D_t(\alpha,\beta,\gamma)$ and compute the derivations of the nontrivial simple finite-dimensional…
The main purpose of this paper is to study the class of Jacobi-Jordan-admissible algebras, such that its product is an anti-biderivation of the related Jacobi-Jordan algebra. We called it as $\mathcal A{\rm BD}$-algebras. First, we provide…
For a conjugation $C$ on a separable, complex Hilbert space $\mathcal{H}$, the set $\mathcal{S}_C$ of $C$-symmetric operators on $\mathcal{H}$ forms a weakly closed, selfadjoint, Jordan operator algebra. In this paper we study…
We construct via Fra\"iss\'e amalgamation an $\omega$-categorical structure whose automorphism group is an infinite oligomorphic Jordan primitive permutation group preserving a `limit of $D$-relations'. The construction is based on a…
We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of simple polarized abelian fourfolds over finite fields. As an application, we compute the Jordan constants of…
Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting modules. Although there are several algorithms for computing this…
We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when…
This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete…
A general discussion of the conformal Ward identities is presented in the context of logarithmic conformal field theory with conformal Jordan cells of rank two. The logarithmic fields are taken to be quasi-primary. No simplifying…
In this paper, we calculate the Jordan decomposition (or say, the Jordan canonical form) for a class of non-symmetric Ornstein-Uhlenbeck operators with the drift coefficient matrix being a Jordan block and the diffusion coefficient matrix…
The three-algebras used by Bagger and Lambert in N=6 theories of ABJM type are in one-to-one correspondence with a certain type of Lie superalgebras. We show that the description of three-algebras as generalized Jordan triple systems…
Jordan, Wigner and von Neumann classified the possible algebras of quantum mechanical observables, and found they fell into 4 "ordinary" families, plus one remarkable outlier: the exceptional Jordan algebra. We point out an intriguing…
In this article we prove that the elliptic, hyperbolic and nilpotent (or unipotent) additive (or multiplicative) Jordan components of an endomorphism $X$ (or an isomorphism $g$) of a finite dimensional vector space are given by polynomials…
Velasquez and Felipe recently introduced quasi-Jordan algebras based on the product $a \triangleleft b = \tfrac12 ( a \dashv b + b \vdash a )$ in an associative dialgebra with operations $\dashv$ and $\vdash$. We determine the polynomial…
Jordan isomorphisms of rings are defined by two equations. The first one is the equation of additivity while the second one concerns multiplicativity with respect to the so-called Jordan product. In this paper we present results showing…