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In the fifth chapter,we study dipolarizations in some quadratic Lie algebras.Inthe first section,we obtain some results on the classification of dipolarizations in gen-eral quadratic Lie algebras,and prove that there exist dipolarizations in the solvablequadratic Lie algebras whose Cartan subalgebras consist of semisimple elements.

第五章讨论了某些二次李代数的双极化,在第一节中,我们给出了二次李代数的双极化的一些分类结果;特别证明Cartan子代数是由半单元组成的二次李代数上存在双极化,第二节确定了四维扩张Heisenberg代数的所有双极化,在第三节中,我们构造了2n+2维扩张Heisenberg代数的六类双极化,我们发现两个不同于半单李代数情形的有趣事实:(1)在扩张Heisenberg代数上同时存在对称和非对称双极化;(2)对应于扩张Heisenberg代数的双极化的特征元有的是半单的有的是幂零的。

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As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸,那乌黑、忧郁的眼睛,她便会相信,他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失

But because of its youthful corporate culture—most people are hustled out of the door in their mid-40s—it had no one to send.

但是因为该公司年轻的企业文化——大多数员工在40来岁的时候都被请出公司——一时间没有好的人选。