Cohomology and duality for coalgebras over a quadratic operad (Q1018552)

Given a finitely generated quadratic operad \(\mathcal P\) and a finitely dimensional \(\mathcal P\)-coalgebra \(V\) the authors define cohomology of \(V\) with coefficients in itself and show that it has the structure of a graded Lie algebra. They also show that this Lie algebra is isomorphic to the cohomology of the dual \(\mathcal P\)-algebra of \(V\) defined by \textit{D. Balavoine} [J. Pure Appl. Algebra 132, No. 3, 221--258 (1998; Zbl 0967.18004)].