Pre-Jordan algebras were introduced recently in analogy with preLie algebras. A pre-Jordan algebra is a vector space A with a bilinear multiplication x · y such that the product x ◦ y = x · y + y · x endows A with the structure of a Jordan algebra, and the left multiplications L·(x) : y 7→ x · y define a representation of this Jordan algebra on A. Equivalently, x ·y satisfies these multilinear ...

Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.

In this paper, we extend the concept of pseudomonotonicity from Rn to the setting of Euclidean Jordan algebras. We study interconnections between pseudomonotonicity, monotonicity, and the Z-property.

In this paper, we extend the concept of pseudomonotonicity from Rn to the setting of Euclidean Jordan algebras. We study interconnections between pseudomonotonicity, monotonicity, and the Z-property.

In this paper, we construct six families of infinite simple conformal superalgebra of finite growth based on our earlier work on constructing vertex operator superalgebras from graded assocaitive algebras. Three subfamilies of these conformal superalgebras are generated by simple Jordan algebras of types A, B and C in a certain sense.

The characterization of automorphisms of Bernstein algebras is an open problem. We only know some particular results. Previously we have characterized the automorphisms of quasiorthogonal, orthogonal, and strongly orthogonal weak Bernstein-Jordan algebras. In this paper we work on the minimal dimension with respect to quasiorthogonality, orthogonality, and strong orthogonality. We establish som...

Let $ {\mathcal{A}} be a unital \ast -algebra containing nontrivial projection. Under some mild conditions on , it is shown that map \Phi:{\mathcal{A}}\rightarrow{\mathcal{A}} nonlinear mixed Jordan triple * -derivation if and only \Phi an additive -derivation. In particular, we apply the above result to prime -algebras, von Neumann algebras with no central summands of type I_{1} factor algebra...

This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting oper...