Filippov代数的上同调与一个类似的Whitehead引理
Cohomology of Filippov algebras and an analogue of Whitehead's lemma
摘要：
我们证明了半单李代数的两个上同调性质也适用于Filippov（n-Lie）代数，即半单n-Lie代数不允许非平凡的中心扩张，它们是刚性的，即，在Gerstenhaber意义上不能变形。这个结果是Filippov代数的Whitehead引理的类似。最后对n-Leibniz代数的情形作了一些评论。
英文摘要：
We show that two cohomological properties of semisimple Lie algebras also hold for Filippov (n-Lie) algebras, namely, that semisimple n-Lie algebras do not admit non-trivial central extensions and that they are rigid i.e., cannot be deformed in Gerstenhaber sense. This result is the analogue of Whitehead's Lemma for Filippov algebras. A few comments about the n-Leibniz algebras case are made at the end.
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