Communications in Algebra | 2021
Coderivations, abelian extensions and cohomology of Lie coalgebras
Abstract
Abstract For any Lie coalgebra with a Lie comodule, a cohomology is constructed by using a subcomplex of the Chevalley–Eilenberg cochain complex of the dual Lie algebra. It is shown that the first (resp. the second) order cohomology group is the space of outer coderivations (resp. the space of equivalent classes of abelian extensions of the Lie coalgebra by its comodule).