  The known equivalence of 8-dimensional chiral spinors and vectors, also
referred to as triality, is discussed for (4+4)-space. Split octonionic
representation of SO(4,4) and Spin(4,4) groups and the trilinear invariant form
are explicitly written and compared with Clifford algebraic matrix
representation. It is noted that the complete algebra of split octonionic basis
units can be recovered from the Moufang and Malcev relations for the three
vector-like elements. Lagrangians on split octonionic fields that generalize
Dirac and Maxwell systems are constructed using group invariant forms. It is
shown that corresponding equations are related to split octonionic analyticity
conditions.
