Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homological properties of parafree Lie algebras   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
$H_2$.

3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex