  An even Artin group is a group which has a presentation with relations of the
form $(st)^n=(ts)^n$ with $n\ge 1$. With a group $G$ we associate a Lie
$\mathbb Z$-algebra $\mathcal{TG}r(G)$. This is the usual Lie algebra defined
from the lower central series, truncated at the third rank. For each even Artin
group $G$ we determine a presentation for $\mathcal{TG}r(G)$. Then we prove a
criterion to determine whether two Coxeter matrices are isomorphic. Let
$c,d\in\mathbb N$ such that $c\ge1$, $d\ge2$ and $\gcd(c,d)=1$. We show that,
if two even Artin groups $G$ and $G'$ having presentations with relations of
the form $(st)^n=(ts)^n$ with $n\in\{c\}\cup\{d^k\mid k\ge1\}$ are such that
$\mathcal{TG}r(G)\simeq\mathcal{TG}r(G')$, then $G$ and $G'$ have the same
presentation up to permutation of the generators. On the other hand, we show an
example of two non-isomorphic even Artin groups $G$ and $G'$ such that
$\mathcal{TG}r(G)\simeq\mathcal{TG}r(G')$.
