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arXiv · 1908.04608

Homological properties of parafree Lie algebras

Sergei O. Ivanov·Roman Mikhailov·Anatoly Zaikovski
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Abstract

In this paper, an explicit construction of a countable parafree Lie algebra over $\mathbb Z/2$ 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 $\mathbb Z$ is greater than two. Moreover, it is proven that there exists a countable parafree group with nontrivial $H_2$.

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Sergei O. Ivanov, Roman Mikhailov, Anatoly Zaikovski. 2019-08-13. Homological properties of parafree Lie algebras. https://doi.org/10.1016/j.jalgebra.2020.05.031

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