单局部有限李代数的内理想
Inner Ideals of Simple Locally Finite Lie Algebras
摘要：
描述了特征为0的代数闭域上单局部有限维李代数的内理想。特别地，证明了一个简单的局部有限维李代数具有非零真内理想当且仅当它是对角型的。利用包络代数的左、右理想刻画了对角型李代数的正则内理想。刻画了有限单李代数的正则内理想。
英文摘要：
Inner ideals of simple locally finite dimensional Lie algebras over an algebraically closed field of characteristic 0 are described. In particular, it is shown that a simple locally finite dimensional Lie algebra has a non-zero proper inner ideal if and only if it is of diagonal type. Regular inner ideals of diagonal type Lie algebras are characterized in terms of left and right ideals of the enveloping algebra. Regular inner ideals of finitary simple Lie algebras are described.
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