Axioms

Colour algebras are noncommutative Jordan algebras and closely related to octonion algebras. They initially emerged in physics since the multiplication of a colour algebra over the real or complex numbers describes the colour symmetry of the Gell–Mann quark model. Over fields of characteristic not equal to two, their structure is now well-known. We initiate the study of colour algebras over a unital commutative base ring R where two is an invertible element, and show when colour algebras can be constructed canonically by employing nondegenerate ternary hermitian forms with trivial determinant. We investigate their structure, their automorphism group and their derivations. We show that there is again a close connection between the colour algebras obtained from hermitian forms and certain types of octonion algebras.

Let $\mathcal{A}$ be a unital ∗-algebra over the complex field $\mathbb{C}$, and let $\mathsf{\Psi }={\left\{{\psi }_m\right\}}_{m\in \mathbb{N}}$ be a nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivation satisfies the relation where and for all with . We demonstrate that every such higher derivation $\mathsf{\Psi }={\left\{{\psi }_m\right\}}_{m\in \mathbb{N}}$ is an additive higher ∗-derivation. As an application, we use this result to characterize the structure of nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivations on a class of typical unital ∗-algebras, including standard operator algebras and von Neumann factors. This result also generalizes several existing results, in particular those concerning nonlinear mixed bi-skew Jordan-type and skew Jordan derivations on unital ∗-algebras.

This paper investigates a fractional diffusion equation incorporating a three-parameter damping. By employing a generalized Mittag–Leffler function alongside the associated Riemann–Liouville resolvent family, we establish the well-posedness of strong solutions. This model extends the classical two-parameter undamped case, thereby ensuring consistency with the existing theoretical framework.