Homological properties of parafree Lie algebras

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 $H_2$.

References in corpus (2)

• A finite Q-bad space
• On discrete homology of a free pro-$p$-group

Cited by in corpus (1)

• Parafree augmented algebras and Gröbner-Shirshov bases for complete augmented algebras