2019/09/02 by Luis Paris, Paris, Luis, Rubén Blasco-García +1
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1909.00572
openalex publication_date 2019/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An even Artin group is a group which has a presentation with relations of the form (st)n=(ts)n with n≥ 1. With a group G we associate a Lie \mathbb Z-algebra TGr(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 TGr(G). Then we prove a criterion to determine whether two Coxeter matrices are isomorphic. Let c,d∈\mathbb N such that c≥1, d≥2 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∈\c\∪\dk| k≥1\ are such that TGr(G)\simeqTGr(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 TGr(G)\simeqTGr(G').