@Article{CMR-31-229, author = {Yu-E and Zhao and and 18639 and and Yu-E Zhao}, title = {Co-Splitting of Simple Lie Algebras of Type $A$, $D$, $E$}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {3}, pages = {229--241}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.03.05}, url = {http://global-sci.org/intro/article_detail/cmr/18925.html} }