2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130151We define a new class of quantum vertex algebras, based on the Hopf algebra $H_D=\mathbb{C}[D]$ of "infinitesimal translations" generated by $D$. Besides the braiding map describing the obstruction to commutativity of products of vertex operators, $H_D$-quantum vertex algebras have as main new ingredient a "translation map" that describes the obstruction of vertex operators to satisfying translation covariance. The translation map also appears as obstruction to the state-field correspondence being a homomorphism. We use a bicharacter construction of Borcherds to construct a large class of $H_D$-quantum vertex algebras. One particular example of this construction yields a quantum vertex algebra that contains the quantum vertex operators introduced by Jing in the theory of Hall-Littlewood polynomials.46 pagesQuantum AlgebraMathematical Physics17B69text