Co-Splitting of Simple Lie Algebras of Type $A$, $D$, $E$ (Communications in Mathematical Research, 2021)
In this paper, through a meticulous description of finite root system,a concrete comultiplication with an explicit action on the basis elements of finitedimensional simple Lie algebras of type $A$, $D$, $E$ is constructed. Then any finitedimensional simple Lie algebra of type $A$, $D$, $E$ is endowed with a new generalizedLie coalgebra splitting. This construction verifies the known existence of a co-splitLie structure on any finite dimensional complex simple Lie algebra.