Global Plemelj Formula of Slice Dirac Operator in Octonions with Complex Spine

Slice analysis is generalized to the setting of octonions with new book structure whose spine consists of a complex plane instead of the real axis. The theory leads to the study of the slice Dirac operator. The associated Cauchy type kernel turns out to be operator-valued rather than function-valued, in contrast to the associative case. The global Plemelj jump formula is established on the boundary of any axially symmetric domain of octonions.