  Motivated by the mathematic theory of split-complex numbers (or hyperbolic
numbers, also perplex numbers) and the split-quaternion numbers (or
coquaternion numbers), we define the notion of split-complex scalar field and
the split-quaternion scalar field. Then we explore the cosmic evolution of
these scalar fields in the background of spatially flat
Friedmann-Robertson-Walker Universe. We find that both the quintessence field
and the phantom field could naturally emerge in these scalar fields.
Introducing the metric of field space, these theories fall into a subclass of
the multi-field theories which have been extensively studied in inflationary
cosmology.
