$H_D$-Quantum Vertex Algebras
  We discuss a class of quantum vertex algebras where not only the commutativity of the vertex algebra is broken by a braiding map $S^{(\tau)}$, but also the translation covariance is broken by a translation map $S^{(\gamma)}$. The new class of quantum vertex operators satisfy a Braided Jacobi Identity containing both the braiding and the translation maps. 
Maarten Bergvelt