  Motivated by the fact that the Hopf-cyclic (co)homologies of function
algebras over Lie groups and universal enveloping algebras over Lie algebras
capture the Lie group and Lie algebra (co)homologies, we hereby upgrade the
classical van Est isomorphism to ones between the Hopf-cyclic (co)homologies of
quantized algebras of functions and quantized universal enveloping algebras,
both in $h$-adic and $q$-deformation frameworks.
