In a previous paper the author defined certain elements of the braid group and showed that they satisfy the analogue of well-known \(q\)-identities such as Pascal's, Vandermonde's, and Cauchy's. These correspond to the one-dimensional representations of \(B_n\). Higher-dimensional representations yield new realizations of these identities. Moreover, some particular higher-dimensional representations are relevant to the definition of quantum groups. The author exploits this observation to define a quantum group from any integer square matrix which coincides with Drinfeld's and Jimbo's definition when the matrix is a symmetric Cartan matrix.