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Lie Subalgebras in a Certain Operator Lie Algebra with Involution 被引量:1
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作者 Shan Li SUN Xue Feng MA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第8期1521-1534,共14页
We show in a certain Lie-algebra, the connections between the Lie subalgebra G+ := G-t-G* 4- [G, G*], generated by a Lie subalgebra G, and the properties of G. This allows us to investigate some useful information... We show in a certain Lie-algebra, the connections between the Lie subalgebra G+ := G-t-G* 4- [G, G*], generated by a Lie subalgebra G, and the properties of G. This allows us to investigate some useful information about the structure of such two Lie subalgehras. Some results on the relations between the two Lie subalgebras are obtained. As an application, we get the following conclusion: Let ,4 C /3(2d) be a space of self-adjoint operators and L: := A ~ i^4 the corresponding complex Lie*-algebra. G+ = G 4- G* 4- [G, G*] and G are two LM-decomposable Lie subalgebras of L: with the decomposition 6+ = 7^(6+) 4- S, G -- T~~ 4- 86, and T^6 C T^(6+). Then 6+ is ideally finite iff T~ := 7~6 4- ~ 4- [T^6,7~] is a quasisolvable Lie subalgebra, S^- := 86 4- S~ 4- [$6, $~] is an ideally finite semisimple Lie subalgebra, and [7~6,86] = [R.~, 86] = {0}. 展开更多
关键词 Skew operator generalized scalar operator E-solvable Lie algebra ideally finite
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