article

Title: Algebraic properties of the module of slice regular functions in several quaternionic variables

Authors: Fabrizio Colombo, Irene Sabadini and Daniele Struppa

Issue: Volume 61 (2012), Issue 4, 1581-1602

Abstract:

$In this paper we define the notion of slice regularity for several quaternionic variables by employing the recent definition due to Ghiloni and Perotti in one variable [R. Ghiloni and A. Perotti, \textit{Slice regular functions on real alternative algebras}, Adv. Math. \textbf{226} (2011), no. 2, 1662--1691]. We show that in the case of several variables slice regularity is equivalent to being solutions of intertwined Cauchy-Riemann type operators, and we give an algebraic treatment of these functions. We also sketch how to extend our ideas to the case of higher dimension.$