Parole chiave
Abstract $\mathbb{Z}_3$-graded Clifford algebras were developed having in mind concrete applications in physics, such as quarks and hypersymmetry, or the $N$-body problem. In this talk we discuss the main ingredients for the study of Dirac operators in this setting: the Howe duality, the Fischer decomposition and the Cauchy-Kovalevskaya extension. By passing, we also will discuss - time permits - possible applications.