Octonion Analysis of Several Variables

Haiyan Wang , Guangbin Ren

Communications in Mathematics and Statistics ›› 2014, Vol. 2 ›› Issue (2) : 163 -185.

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Communications in Mathematics and Statistics ›› 2014, Vol. 2 ›› Issue (2) : 163 -185. DOI: 10.1007/s40304-014-0034-x
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Octonion Analysis of Several Variables

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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.

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Several octonionic variables / Bochner–Martinelli formula / Hartogs theorem / Non-homogenous Cauchy–Riemann equations

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Haiyan Wang, Guangbin Ren. Octonion Analysis of Several Variables. Communications in Mathematics and Statistics, 2014, 2(2): 163-185 DOI:10.1007/s40304-014-0034-x

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