On the cohomology of Coxeter groups
نویسندگان
چکیده
منابع مشابه
Cohomology and Euler Characteristics of Coxeter Groups
Coxeter groups are familiar objects in many branches of mathematics. The connections with semisimple Lie theory have been a major motivation for the study of Coxeter groups. (Crystallographic) Coxeter groups are involved in Kac-Moody Lie algebras, which generalize the entire theory of semisimple Lie algebras. Coxeter groups of nite order are known to be nite re ection groups, which appear in in...
متن کاملCohomology computations for relatives of Coxeter groups
We compute the group cohomology H∗(G;ZG) or the reduced L-cohomology, H∗(G;L2G) when G is either • a graph product of infinite groups, • an Artin group, or • a Bestvina-Brady group. The proofs will appear in [8]. Suppose (W,S) is a Coxeter system. A subset T ⊂ S is spherical if it generates a finite subgroup of W . Let S denote the poset of spherical subsets of S. The nerve of (W,S) is the simp...
متن کاملWeighted L–cohomology of Coxeter groups
Given a Coxeter system .W;S/ and a positive real multiparameter q , we study the “weighted L–cohomology groups,” of a certain simplicial complex † associated to .W;S/ . These cohomology groups are Hilbert spaces, as well as modules over the Hecke algebra associated to .W;S/ and the multiparameter q . They have a “von Neumann dimension” with respect to the associated “Hecke–von Neumann algebra” ...
متن کاملWeighted L–cohomology of Coxeter groups based on barycentric subdivisons
Associated to any finite flag complex L there is a right-angled Coxeter group WL and a contractible cubical complex ΣL (the Davis complex) on which WL acts properly and cocompactly, and such that the link of each vertex is L. It follows that if L is a generalized homology sphere, then ΣL is a contractible homology manifold. We prove a generalized version of the Singer Conjecture (on the vanishi...
متن کاملEssays 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2001
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(00)00115-8