Lie-Rinehart bialgebras for crossed products

Let g be a Lie algebra over a field K. Endow the polynomial ring K[t] with a g-action by derivations and consider the resulting crossed product K[t] circle dot(theta) g in the category of (K, K[t])-Lie algebras. We explore Lie-Rinehart bialgebra structures on (K[t], K [t] circle dot(theta) g) that arise via compatible pairs and epsilon-dynamical r-matrices. We give a complete classification for g = sl(2, K). (C) 2010 Elsevier B.V. All rights reserved.Mathematics, AppliedMathematicsSCI(E)0ARTICLE61270-128321