Starting with a canonical symplectic structure defined on the cotangent bundle T ∗ G we derive, via Dirac hamiltonian reduction, Poisson brackets (PBs) on an arbitrary infinite-dimensional group G (admitting central extension). The PB structures are given in terms of an r -operator kernel related to the two-cocycle of the underlying Lie algebra and satisfying a differential classical Yang-Baxter equation. The explicit expressions of the PBs among the group variables for the ( N ,0) for N =0, 1,…, 4 (super-) Virasoro groups and the group of area-preserving diffeomorphisms on the torus are presented.