Semi-edges, reflections and Coxeter groups
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- by Ralf Gramlich, Georg W. Hofmann and Karl-Hermann Neeb PDF
- Trans. Amer. Math. Soc. 359 (2007), 3647-3668 Request permission
Abstract:
We combine the theory of Coxeter groups, the covering theory of graphs introduced by Malnic, Nedela and Skoviera and the theory of reflections of graphs in order to obtain the following characterization of a Coxeter group: Let $\pi : \Gamma \rightarrow (v,D,\iota ,-1)$ be a $1$-covering of a monopole admitting semi-edges only. The graph $\Gamma$ is the Cayley graph of a Coxeter group if and only if $\pi$ is regular and any deck transformation in $\Delta (\pi )$ that interchanges two neighboring vertices of $\Gamma$ acts as a reflection on $\Gamma$.References
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Additional Information
- Ralf Gramlich
- Affiliation: TU Darmstadt, FB Mathematik / AG 5, Schloßgartenstraße 7, 64289 Darmstadt, Germany
- Email: gramlich@mathematik.tu-darmstadt.de
- Georg W. Hofmann
- Affiliation: TU Darmstadt, FB Mathematik / AG 5, Schloßgartenstraße 7, 64289 Darmstadt, Germany
- Address at time of publication: 5669 Merkel Street, Halifax, Nova Scotia B3K 2J1, Canada
- Email: ghofmann@mathematik.tu-darmstadt.de, hofmann@mathstat.dal.ca
- Karl-Hermann Neeb
- Affiliation: TU Darmstadt, FB Mathematik / AG 5, Schloßgartenstraße 7, 64289 Darmstadt, Germany
- MR Author ID: 288679
- Email: neeb@mathematik.tu-darmstadt.de
- Received by editor(s): October 27, 2004
- Received by editor(s) in revised form: March 22, 2005
- Published electronically: March 7, 2007
- © Copyright 2007 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 3647-3668
- MSC (2000): Primary 05C25, 20F55, 55U10
- DOI: https://doi.org/10.1090/S0002-9947-07-04040-8
- MathSciNet review: 2302510