Subalgebra generated by ad-locally nilpotent elements of Borcherds generalized Kac-Moody Lie algebras (Q2068140)

The paper consider a Borcherds Generalized Kac-Moody Lie algebra \({\mathfrak{g}}(A)\) (or GKM) where \(A\) is a symmetrizable, indecomposable Cartan matrix. Let \({\mathfrak{g}}_{nil}\) be the Lie subalgebra generated by those \(x\in \mathfrak{g}\) such that ad\(x\) acts nilpotently on \(\mathfrak{g}\). Then \[ {\mathfrak{g}}'(B)\subset {\mathfrak{g}}_{nil}\subset {\mathfrak{g}}'(B)+\mathfrak{h}, \] where \(B\subset A\) is the submatrix parametrized by those \(i\) such that \(a_{ii}=2\), i.e., \(\alpha_i\) is a real root and \(\mathfrak{g}'(B)\) is the derived algebra of \({\mathfrak{g}}(B)\).