Wells sequences for abelian extensions of Lie coalgebras

Abstract

For a Lie comodule [Formula: see text] of a Lie coalgebra [Formula: see text] and the Lie algebra [Formula: see text] (respectively, the group [Formula: see text]) of diagonal coderivations (respectively, Lie coalgebra automorphisms) of the semidirect sum [Formula: see text], we show that there is a representation of [Formula: see text] (respectively, [Formula: see text]) on the second cohomology group [Formula: see text], from which we construct obstruction classes of extensibility of pairs of coderivations (respectively Lie coalgebra automorphisms) and exact sequences of Wells type for abelian extensions of Lie coalgebras.