Trivial central extensions of Lie bialgebras

FARINATI, MARCO - JANCSA, A. PATRICIA

JOURNAL OF ALGEBRA

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2013 vol. 390 p. 56 - 76

0021-8693

From a Lie algebra g satisfying Z(g)=0 and Λ^2(g)g=0 (in particular, for g semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form L=g×K 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×Kn. In interesting cases we characterize the Lie algebra of biderivations.