Related papers: A Jordan algebra approach to the cubic eiconal equ…

In this note, we observe a relation between dialgebras (in particular, Leibniz algebras) and conformal algebras. The purpose is to show how the methods of conformal algebras help solving problems on dialgebras, and, conversely, how the…

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 extend the loop algebra construction for algebras graded by abelian groups to study graded-simple algebras over the field of real numbers (or any real closed field). As an application, we classify up to isomorphism the graded-simple…

We study finite-dimensional commutative algebras, which satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a classification in dimensions $n<7$ over algebraically closed fields of…

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…

We investigate the canonical pseudo-Riemannian metrics associated with Jordan-analogues of the coadjoint orbits for pseudo-Euclidean Jordan superalgebras.

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…

In this short note we prove that every Jordan derivation of triangular algebras is a derivation.

Let $k$ be a field of characteristic not equal to $2,3$, $\mathbb{O}$ an octonion over $k$ and $\mathcal{J}$ the exceptional Jordan algebra defined by $\mathbb{O}$. We consider the prehomogeneous vector space $(G,V)$ where $G=GE_6\times…

Let $G$ and $H$ be locally compact groups. We will show that each contractive Jordan isomorphism $\Phi\colon L^1(G)\to L^1(H)$ is either an isometric isomorphism or an isometric anti-isomorphism. We will apply this result to study isometric…

We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…

In this paper, we study the class of Jordan dialgebras. We develop an approach for reducing problems on dialgebras to the case of ordinary algebras. It is shown that straightforward generalizations of the classical Cohn's, Shirshov's, and…

Let G be an arbitrary group and let K be a field of characteristic different from 2. We classify the G-gradings on the Jordan algebra of upper triangular matrices of order n over K. It turns out that there are, up to a graded isomorphism,…

We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…

Axial algebras are commutative nonassociative algebras generated by a finite set of primitive idempotents which action on an algebra is semisimple, and the fusion laws on the products between eigenvectors for these idempotents are…

The paper is devoted to the description of the varieties of complex 5-dimensional nilpotent Jordan superalgebras. We find all representatives for the isomorphism classes, using the Jordan normal form, results of simultaneous matrix…

For any positive integer $n$, $n$-derived-simple derived discrete algebras are classified up to derived equivalence. Furthermore, the Jordan-H\"older theorems for all kinds of derived categories of derived discrete algebras are obtained.

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…

We address a Jordan version of Johnson theorem on (associative) algebras of quotients, namely whether a strongly nonsingular (the Jordan version of nonsingularity) has a von Neumann regular algebra of quotients. Although the answer is…

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…