Gleason's problem associated to a real ternary algebra and applications (Q1659526)

This paper deals with the study of a class of regular functions defined on a real ternary algebra. After a description and some remarks on ternary algebras, the authors highlight a special basis constructed upon a choice of idempotent elements. This leads them to define two differential operators akin to Cauchy-Riemann(-Fueter) ones. Afterwards, they study the theory of functions in the kernel of such operators, noticing some similarity with the Fueter theory in the quaternionic case. With the help of Fueter-like variables, they are able to state and prove a Gleason-like theorem. Then they recognize an analyticity behaviour of such regular functions, with respect to Fueter-like variables and, hence, give a characterization of regular rational functions of a Fueter-like variable. In the last part of the paper an application to Drury-Arveson spaces is announced.