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An even Artin group is a group which has a presentation with relations of theform $(st)^n=(ts)^n$ 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 definedfrom the lower central series, truncated at the third rank. For each even Artingroup $G$ we determine a presentation for $\mathcal{TG}r(G)$. Then we prove acriterion 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 ofthe 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 samepresentation up to permutation of the generators. On the other hand, we show anexample of two non-isomorphic even Artin groups $G$ and $G'$ such that$\mathcal{TG}r(G)\simeq\mathcal{TG}r(G')$.

On the isomorphism problem for even Artin groups