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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This work was supported by the NNSF of China (11771412).
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Jin, M., Ren, G. & Sabadini, I. Slice Dirac operator over octonions. Isr. J. Math. 240, 315–344 (2020). https://doi.org/10.1007/s11856-020-2067-z
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DOI: https://doi.org/10.1007/s11856-020-2067-z