Right-angled mock reflection and mock Artin groups

Author:
Richard Scott

Journal:
Trans. Amer. Math. Soc. **360** (2008), 4189-4210

MSC (2000):
Primary 20Fxx

DOI:
https://doi.org/10.1090/S0002-9947-08-04452-8

Published electronically:
March 12, 2008

MathSciNet review:
2395169

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Abstract: We define a *right-angled mock reflection group* to be a group acting combinatorially on a CAT(0) cubical complex such that the action is simply-transitive on the vertex set and all edge-stabilizers are . We give a combinatorial characterization of these groups in terms of graphs with local involutions. Any such graph not only determines a mock reflection group, but it also determines a *right-angled mock Artin group*. Both classes of groups generalize the corresponding classes of right-angled Coxeter and Artin groups. We conclude by showing that the standard construction of a finite space for right-angled Artin groups generalizes to these mock Artin groups.

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Additional Information

**Richard Scott**

Affiliation:
Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, California 95053

Email:
rscott@math.scu.edu

DOI:
https://doi.org/10.1090/S0002-9947-08-04452-8

Received by editor(s):
June 26, 2006

Published electronically:
March 12, 2008

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.