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 - <p style="text-align: justify;">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.</p>