منابع مشابه
Essays on Coxeter groups Coxeter elements in finite Coxeter groups
A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...
متن کاملArtin Groups and Coxeter Groups
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 ...
متن کاملCoxeter Covers of the Classical Coxeter Groups
Let C(T ) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY (T ) be a natural quotient of C(T ), and if C(T ) is simply-laced (which means all the relations between the generators has order 2 or 3), CY (T ) is a generalized Coxeter group, too . Let At,n be a group which contains t Abelian groups generated by n elements. The...
متن کاملCoxeter Groups as Beauville Groups
We generalize earlier work of Fuertes and González-Diez as well as earlier work of Bauer, Catanese and Grunewald by classifying which of the irreducible Coxeter groups are (strongly real) Beauville groups. We also make partial progress on the much more difficult question of which Coxeter groups are Beauville groups in general as well as discussing the related question of which Coxeter groups ca...
متن کاملCoxeter Groups and Asphericalmanifolds
I. Contractible manifolds and aspherical manifolds. Suppose that M n is a compact, contractible n-manifold with boundary. These assumptions imply that the boundary of M has the homology of an (n-l)-sphere; however, they do not imply that it is simply connected. If n ~ 3, then for M n to be homeomorphic to a disk it is obviously necessary that ~M be simply connected. For n ~ 5 this condition is ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2016
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13013