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Symmetrical subgroups of Artin groups

Symmetrical subgroups of Artin groups
Symmetrical subgroups of Artin groups
We show that the subgroup fixed by a group of symmetries of an Artin system (A, S) is itself an Artin group under the hypothesis that the Deligne complex associated to A admits a suitable CAT(0) metric. Such a metric is known to exist for all Artin groups of type FC, which include all the finite type Artin groups as well as many infinite types. We also recover the previously known analogous result for an arbitrary Coxeter system (W, S).
0001-8708
159-177
Crisp, John
85fb6ab7-4793-4801-8dc5-96f883bc88ff
Crisp, John
85fb6ab7-4793-4801-8dc5-96f883bc88ff

Crisp, John (2000) Symmetrical subgroups of Artin groups. Advances in Mathematics, 152 (1), 159-177. (doi:10.1006/aima.1999.1895).

Record type: Article

Abstract

We show that the subgroup fixed by a group of symmetries of an Artin system (A, S) is itself an Artin group under the hypothesis that the Deligne complex associated to A admits a suitable CAT(0) metric. Such a metric is known to exist for all Artin groups of type FC, which include all the finite type Artin groups as well as many infinite types. We also recover the previously known analogous result for an arbitrary Coxeter system (W, S).

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Published date: June 2000

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Local EPrints ID: 29864
URI: http://eprints.soton.ac.uk/id/eprint/29864
DOI: doi:10.1006/aima.1999.1895
ISSN: 0001-8708
PURE UUID: 5fc3f0c3-79aa-46f2-99d8-6450ae0b74e0

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Date deposited: 28 Jan 2009
Last modified: 15 Mar 2024 07:35

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Author: John Crisp

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