  The nonassociativity of the octonion algebra necessitates a bimodule
representation, in which each element is represented by a left and a right
multiplier. This representation can then be used to generate gauge
transformations for the purpose of constructing a field theory symmetric under
a gauged octonion algebra, the nonassociativity of which appears as a failure
of the representation to close, and hence produces new interactions in the
gauge field kinetic term of the symmetric Lagrangian.
