Poisson Structures on the Poincaré Group

An introduction to inhomogeneous Poisson groups is given. Poisson inhomogeneous O(p,q) are shown to be coboundary, the generalized classical Yang-Baxter equation having only a one-dimensional right-hand side. Normal forms of the classical r-matrices for the Poincaré group (inhomogeneous O(1,3)) are calculated. Received: 19 February 1996 / Accepted: 10 September 1996