Weak amenability of right-angled Coxeter groups
نویسندگان
چکیده
منابع مشابه
Weak amenability of Coxeter groups
Let (G,S) be a Coxeter group. We construct a continuation, to the open unit disc, of the unitary representations associated to the positive definite functions g 7→ rl(g). (Here 0 < r < 1, and l denotes the length function with respect to the generating set S.) The constructed representations are uniformly bounded and we prove that this implies the weak amenability of the group G. Résumé Soit (G...
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If W is a right-angled Coxeter group, then the group Aut(W ) of automorphisms of W acts on the set of conjugacy classes of involutions in W. Following Tits [16], the kernel of this action is denoted by Aut◦(W ). Since W is a CAT(0) group [12], the index of Aut◦(W ) in Aut(W ) is finite and there is a series 1 Inn(W ) Aut◦(W ) Aut(W ) of normal subgroups of Aut(W ). A presentation for Aut◦(W ) w...
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If (W, S) is a right-angled Coxeter group, then Aut(W ) is a semidirect product of the group Aut◦(W ) of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, Aut◦(W ) is a semidirect product of Inn(W ) by the quotient Out◦(W ) = Aut◦(W )/Inn(W ). We also give sufficient conditions for the compatibility of the two semidirect products. When...
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In mathematics, a group is the set of symmetries of an object. Coxeter groups are a broad and natural class of groups that are related to reflectional symmetries. Each Coxeter group is determined by a diagram, called a labeled graph, that encodes algebraic information about the group. In general, two different labeled graphs can give rise to the same group. It is therefore natural to ask: are t...
متن کاملA Complex for Right-angled Coxeter Groups
We associate to each right-angled Coxeter group a 2-dimensional complex. Using this complex, we show that if the presentation graph of the group is planar, then the group has a subgroup of finite index which is a 3-manifold group (that is, the group is virtually a 3-manifold group). We also give an example of a right-angled Coxeter group which is not virtually a 3-manifold group.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1993-1172955-8