We introduce oriented tree diagram Lie algebras which are generalized from Xu＇s both upward and downward tree diagram Lie algebras, and study certain numerical invariants of these algebras related to abelian ideals.
Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In ...Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of Ь.展开更多
基金Supported by Shanghai Leading Academic Discipline Project (Project No.B407)
文摘We introduce oriented tree diagram Lie algebras which are generalized from Xu＇s both upward and downward tree diagram Lie algebras, and study certain numerical invariants of these algebras related to abelian ideals.
基金Supported by the Doctor Foundation of Henan Polytechnic University(B2010-93)Supported by the National Natural Science Foundation of China(11126121)+2 种基金Supported by the Natural Science Foundation of Henan Province(112300410120)Supported by the Natural Science Research Program of Education Department of Henan Province(201lB110016)Supported by the Applied Mathematics Provincial-level Key Discipline of Henan Province of Henau Polytechuic University
文摘Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of Ь.
