Commun. Math. Res., 31 (2015), pp. 229-241.
Published online: 2021-05
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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} }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.