Trivial central extensions of Lie bialgebras - Farinati, Marco Andrés (2013)
From a Lie algebra g satisfying Z(g)=0 and Λ2(g)g=0 (in particular, for g semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form L=g×Kdouble-struck in terms of Lie bialgebra structures on g (not necessarily factorizable nor quasi-triangular) and its biderivations, for any field K of characteristic different form 2, 3. If moreover, [g,g]=g, then we describe also all Lie bialgebra structures on extensions L=g×Kdouble-struckn. In interesting cases we characterize the Lie algebra of biderivations. © 2013 Elsevier Inc.