Generalized WDVV equations for B_r and C_r pure N=2 Super-Yang-Mills theory

A proof that the prepotential for pure N = 2 Super-Yang–Mills theory associated with Lie algebras B r and C r satisfies the generalized WDVV (Witten–Dijkgraaf–Verlinde–Verlinde) system was given by Marshakov, Mironov, and Morozov. Among other things, they use an associative algebra of holomorphic differentials. Later Itô and Yang used a different approach to try to accomplish the same result, but they encountered objects of which it is unclear whether they form structure constants of an associative algebra. We show by explicit calculation that these objects are none other than the structure constants of the algebra of holomorphic differentials.