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- W4288125142 abstract "An even Artin group is a group which has a presentation with relations of the form $(st)^n=(ts)^n$ with $nge 1$. 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 $c,dinmathbb N$ such that $cge1$, $dge2$ 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 $nin{c}cup{d^kmid kge1}$ are such that $mathcal{TG}r(G)simeqmathcal{TG}r(G')$, 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 $mathcal{TG}r(G)simeqmathcal{TG}r(G')$." @default.
- W4288125142 created "2022-07-28" @default.
- W4288125142 creator A5054400690 @default.
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- W4288125142 date "2019-09-02" @default.
- W4288125142 modified "2023-09-26" @default.
- W4288125142 title "On the isomorphism problem for even Artin groups" @default.
- W4288125142 doi "https://doi.org/10.48550/arxiv.1909.00572" @default.
- W4288125142 hasPublicationYear "2019" @default.
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