Semi-edges, reflections and Coxeter groups

Gramlich R, Hofmann GW, Neeb KH (2007)

Publication Type: Journal article, Original article

Publication year: 2007

Journal

Transactions of the American Mathematical Society American Mathematical Society

Publisher: American Mathematical Society

Book Volume: 359

Pages Range: 3647-3668

Journal Issue: 08

DOI: 10.1090/S0002-9947-07-04040-8

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 -> ( v, D, i, -1) be a 1-covering of a monopole admitting semiedges only. The graph G 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.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Technische Universität Darmstadt DE Germany (DE)

How to cite

APA:

Gramlich, R., Hofmann, G.W., & Neeb, K.H. (2007). Semi-edges, reflections and Coxeter groups. Transactions of the American Mathematical Society, 359(08), 3647-3668. https://dx.doi.org/10.1090/S0002-9947-07-04040-8

MLA:

Gramlich, Ralf, Georg W. Hofmann, and Karl Hermann Neeb. "Semi-edges, reflections and Coxeter groups." Transactions of the American Mathematical Society 359.08 (2007): 3647-3668.

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