We are concerned with the question when Hom-Lie structures on a Lie algebra closed respect to Jordan product. Somewhat unexpectedly, this leads us certain questions connected Yang-Baxter equation, and decomposition of into sum subalgebras given properties.

In this note, we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real Jordan algebra. We use this formula as an inspiration for a similar recursive formula involving the Jack polynomials.

We show that a quaternary Jordan derivation on a quaternary Banach algebra associated with the equation f( x+ y + z 4 ) + f( 3x− y − 4z 4 ) + f( 4x+ 3z 4 ) = 2f(x) . is satisfied in generalized Hyers–Ulam stability.

Let g be a finite dimensional Lie algebra over a field k of characteristic zero. An element x of g is said to have an abstract Jordan-Chevalley decomposition if there exist unique s, n ∈ g such that x = s + n, [s, n] = 0 and given any finite dimensional representation π : g → gl(V ) the Jordan-Chevalley decomposition of π(x) in gl(V ) is π(x) = π(s) + π(n). In this paper we prove that x ∈ g has...

We prove that every 2-local derivation from the algebra Mn(A)(n > 2) into its bimodule Mn(M) is a derivation, where A is a unital Banach algebra and M is a unital A-bimodule such that each Jordan derivation from A into M is an inner derivation, and that every 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie d...