TY - JOUR T1 - Co-Splitting of Simple Lie Algebras of Type $A$, $D$, $E$ AU - Zhao , Yu-E JO - Communications in Mathematical Research VL - 3 SP - 229 EP - 241 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.03.05 UR - https://global-sci.org/intro/article_detail/cmr/18925.html KW - Lie coalgebra, co-splitting, finite-dimensional simple Lie algebra. AB -

In this paper, through a meticulous description of finite root system, a concrete comultiplication with an explicit action on the basis elements of finite dimensional simple Lie algebras of type $A$, $D$, $E$ is constructed. Then any finite dimensional simple Lie algebra of type $A$, $D$, $E$ is endowed with a new generalized Lie coalgebra splitting. This construction verifies the known existence of a co-split Lie structure on any finite dimensional complex simple Lie algebra.