Co-splitting of Simple Lie Algebras of Type A, D, E  

作　　者：Zhao Yu-e Du Xian-kun 

机构地区：[1]School of Mathematics, Qingdao University

出　　处：《Communications in Mathematical Research》2015年第3期229-241,共13页数学研究通讯（英文版）

基　　金：The Anhui Province College Excellent Young Talents Fund(2013SQRL071ZD)

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

关 键 词：Lie coalgebra co-splitting finite-dimensional simple Lie algebra 

分 类 号：O152.5[理学—数学] O562.1[理学—基础数学]