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arXiv · 1908.01383

Slice Dirac operator over octonions

Ming Jin·Guangbin Ren·Irene Sabadini
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Abstract

The slice Dirac operator over octonions is a slice counterpart of the Dirac operator over quaternions. It involves a new theory of stem functions, which is the extension from the commutative $ O(1) $ case to the non-commutative $ O(3) $ case. For functions in the kernel of the slice Dirac operator over octonions, we establish the representation formula, the Cauchy integral formula (and, more in general, the Cauchy-Pompeiu formula), and the Taylor as well as the Laurent series expansion formulas.

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Ming Jin, Guangbin Ren, Irene Sabadini. 2019-08-04. Slice Dirac operator over octonions. https://arxiv.org/abs/1908.01383

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