Riemann slice-domains over quaternions I

Xinyuan Dou; Guangbin Ren

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arXiv · 1808.06994

Riemann slice-domains over quaternions I

Xinyuan Dou·Guangbin Ren

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Abstract

We construct a counterexample to a well-known extension theorem for slice regular functions, which motivates us to develop a theory of Riemann slice-domains by introducing a new topology on quaternions. By some paths describing axial symmetry in Riemann slice-domains, we rectify the classical extension formula in the theory of slice regular functions and prove a representation formula over slice-domains of regularity. This proof involves an intertwining relation between imaginary units of quaternions and a fixed matrix corresponding to a complex structure.

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Xinyuan Dou, Guangbin Ren. 2018-08-21. Riemann slice-domains over quaternions I. https://arxiv.org/abs/1808.06994

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