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Symmetrical Subgroups of Artin Groups

✍ Scribed by John Crisp

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 208 KB
Volume: 152
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1999.1895

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✦ Synopsis

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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