2019/12/19 by Rolf Soeren Krausshar, Krausshar, Rolf Soeren
Mathematics · #30 G 35 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1912.09109
openalex publication_date 2019/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we revisit the concept of conformality in the sense of Gauss in\nthe context of octonions and Clifford algebras. We extend a characterization of\nconformality in terms of a system of partial differential equations and\ndifferential forms using special orthonormal sets of continuous functions that\nhave been used before in the particular quaternionic setting. The aim is to\ndescribe to which higher dimensional algebras this characterization can exactly\nbe extended and under which circumstances. It turns out to be crucial that this\ncharacterization requires a domain of definition that lies in a subalgebra that\nhas the norm composition property and that is either associative (Clifford\nalgebra case) or at least alternative (octonionic case). The orthonormal frames\nare elements of the spin group Spin(n+1). We round off by relating the nature\nof the orthonormal frames to the associated M "obius transformation which are\nrelated to SO(9,1) in the octonionic case and to the Ahlfors-Vahlen group in\nthe case of a Clifford algebra.\n