Unified quantization of three-dimensional bialgebras

The joint multiparameter quantization of several three-dimensional Lie algebras is given. Among the quantized algebras one finds the Heisenberg algebra, the algebra of motions of the (pseudo)euclidean plane and $su(2)$. Such a quantization is possible because all of the mentioned algebras are dual to the same solvable Lie algebra. The explicit form of the number $R$-matrix is given which allows to encode some of the commutation relations in the form of the RTT-equation.