Quantum van Est isomorphism

Abstract

Motivated by the fact that the Hopf-cyclic (co)homologies of function algebras over Liegroups and universal enveloping algebras over Lie algebras capture the Lie group and Lie alge-bra (co)homologies, we hereby upgrade the classical van Est isomorphism to ones between theHopf-cyclic (co)homologies of quantized algebras of functions and quantized universal envelopingalgebras, both inh-adic andq-deformation frameworks.