Octonion Analysis of Several Variables

Abstract

The octonions are distinguished in the $$M$$ -theory in which Universe is the usual Minkowski space $${\mathbb {R}}^4$$ times a $$G_2$$ manifold of very small diameter with $$G_2$$ being the automorphism group of the octonions. The multidimensional octonion analysis is initiated in this article, which extends the theory of several complex variables, such as the Bochner–Martinelli formula, the theory of non-homogeneous Cauchy–Riemann equations, and the Hartogs principle, to the non-commutative and non-associative realm.