Algebraic structure of open-string interactions

Starting from the gauge-invariant equations of motion for the free open string we show how to generate interactions by analogy with the Yang-Mills system. We postulate non-Abelian transformation laws acting on the fields of the gauge-invariant free open-string theory. By demanding algebraic closure we then derive a set of consistency requirements and show that they lead to the construction of the minimal interacting equations which contain no cubic terms away from the physical gauge. We present explicit solutions to lowest interacting order for both vertices and structure functions