Second cohomology groups of the Hopf${}^{\ast }$-algebras associated to universal unitary quantum groups

We compute the second (and the first) cohomology groups of ${}^{\ast }$-algebras associated to the universal quantum unitary groups of not neccesarily Kac type, extending our earlier results for the free unitary group $U_d^{+}$. The extended setup forces us to use infinite-dimensional representations to construct the cocycles.