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. ...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.展开更多
基金The Anhui Province College Excellent Young Talents Fund(2013SQRL071ZD)
文摘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.
