Abstract In this paper, an explicit construction of a countable parafree Lie algebra with nonzero second homology is given. It is also shown that the cohomological dimension of the pronilpotent completion of a free noncyclic finitely generated Lie algebra over Z is greater than two. Moreover, it is proven that there exists a countable parafree group with nontrivial H 2 .

中文翻译：

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无序李代数的同调性质

摘要 本文给出了具有非零第二同调的可数无参李代数的显式构造。还表明，自由非循环有限生成李代数在 Z 上的幂幂完成的上同调维数大于 2。此外，证明了存在具有非平凡H 2 的可数parafree 群。