Quantum Heisenberg--Weyl Algebras
  All Lie bialgebra structures on the Heisenberg--Weyl algebra $[A_+,A_-]=M$ are classified and explicitly quantized. The complete list of quantum Heisenberg--Weyl algebras so obtained includes new multiparameter deformations, most of them being of the non-coboundary type. 
Angel Ballesteros, Francisco J. Herranz and Preeti Parashar