Artin Groups and Coxeter Groups
نویسندگان
چکیده
where the words on each side of these relations are sequences of mij letters where ai and aj alternate in the sequence. The matrix of values mij is a Coxeter matrix M = (mij)i,j∈I on I. These groups generalize the braid groups established in 1925 by E. Artin in a natural way and therefore we suggest naming them Artin groups. If one adds the relations ai = 1 to the relations in the presentation of an Artin group then one gets a presentation of a Coxeter group G. Thus the Coxeter groups are quotient groups of the Artin groups. It is well known that in the case of the braid group one gets the symmetric group in this way.
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