Slice Dirac operator over octonions
Complex Variables
2019-12-11 v1
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 case to the non-commutative 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.
Cite
@article{arxiv.1908.01383,
title = {Slice Dirac operator over octonions},
author = {Ming Jin and Guangbin Ren and Irene Sabadini},
journal= {arXiv preprint arXiv:1908.01383},
year = {2019}
}