Year: 2015
Author: Yu-E Zhao
Communications in Mathematical Research , Vol. 31 (2015), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2015.03.05
Communications in Mathematical Research , Vol. 31 (2015), Iss. 3 : pp. 229–241
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Lie coalgebra co-splitting finite-dimensional simple Lie algebra.