Star Reducible Coxeter Groups

Compressed Decision Problems for Graph Products and Applications to (outer) Automorphism Groups

It is shown that the compressed word problem of a graph product of finitely generated groups is polynomial time Turing-reducible to the compressed word problems of the vertex groups. A direct corollary of this result is that the word problem for the automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Moreover, it is shown that a res...

Complete Growth Series of Coxeter Groups with more than Three Generators

M ay 2 00 9 A diagrammatic representation of an affine C Temperley –

In this thesis, I present an associative diagram algebra that is a faithful representation of a particular Temperley–Lieb algebra of type affine C, which has a basis indexed by the fully commutative elements of the Coxeter group of the same type. The Coxeter group of type affine C contains an infinite number of fully commutative elements, and so the corresponding Temperley–Lieb algebra is of in...

On the Isomorphism Problem for Finitely Generated Coxeter Groups. I Basic Matching

The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [3] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. In this paper, we determine some stro...

On the Direct Indecomposability of Infinite Irreducible Coxeter Groups and the Isomorphism Problem of Coxeter Groups

In this paper we prove that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group, without the finite rank assumption. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group W , the centralizers in W of the normal subgroups of W that are generated by involutions. As a consequence, we show that the problem of deciding ...