\(n\)th pointwise inner derivation of \(n\)-isoclinism Lie algebras (Q2041234)

\textit{K. Moneyhun} [Algebras Groups Geom. 11, No. 1, 9--22 (1994; Zbl 0801.17005)] introduced the concept of isoclinism to Lie algebras. The present authors generalize the concept to \(n\)-isoclinism for Lie algebras where they show that when Lie algebras \(L\) and \(H\) are \(n\)-isoclinic then certain subalgebras of \(\mathrm{Der}(L)\) and \(\mathrm{Der}(H)\) are isomorphic. A key role is played by \(\mathrm{Der}_n^c(L)= \{T\in \mathrm{Der}(L)\) such that \(T(x) \in [x,L^n)\) for all \(x\in L\}\). Conditions are found for \(\mathrm{Der}_n^c(L)\) to be isomorphic to certain subalgebras of \(\mathrm{Der}(L)\).