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Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics^[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras. In this paper, we study solvable quadratic Lie algebras. In Section 1, we study quadratic solvable Lie algebras whose Cartan subalgebras consist of semi-simple elements. In Section 2,we present a procedure to construct a class of quadratic Lie algebras, and we can exhaust all solvable quadratic Lie algebras in such a way. All Lie algebras mentioned in this paper are finite dimensional Lie algebras over a field F of characteristic 0. 相似文献
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本文对广义Kao-Moody代数的根的性质作了一些研究,并完全刻划了正虚根集,在一定条件之下,得到了某一正虚根集成为半群的充要条件。 相似文献
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The singular behaviour in the vicinity of intersection between the body and free surface is presented.It is shown that in the linear regime the singularity of velocity potential for transient problem is in d~2|nd.The singular behaviour for harmonic problem is the same as the result for the transient problem.In particular,the singularity for the harmonic problem with infinite frequency is in d~2 lnd for velocity potential(d is the distance between field point and intersection). 相似文献
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ALiealgebraiscalledsplittableifboththesendshoplepartandthenilpotelltpartofitsinnerderivationarestillixmerderivations.OnecanprovethstaalgebraicLiealgebra(specially,acompleteLiealgebra)issplittable.Itseemsnaturaltoinvestigatefurtherpropertiesofthesplit... 相似文献
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浮体与自由面交线附近流场的奇异性 总被引:2,自引:0,他引:2
本文研究了浮体与自由面交线附近势流流场的奇异性。结果表明,线性时域解在交线附近的奇异特征是d2lnd.线性频域解在交线附近的奇异特征也是d2lnd,但若采用无穷大频率自由面条件φ=0,交线附近流场的奇异特征是d1nd,这里的d表示交线上的点与场点的距离。 相似文献