English

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 O(1) O(1) case to the non-commutative O(3) 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.

Keywords

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}
}