Rigidity of Coxeter Groups and Artin Groups |
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Authors: | Noel Brady Jonathan P McCammond Bernhard Mühlherr Walter D Neumann |
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Institution: | (1) Department of Mathematics, University of Oklahoma, Norman, OK, 73019, U.S.A.;(2) Department of Mathematics, University of California, Santa Barbara, CA, 93106, U.S.A.;(3) Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany;(4) Department of Mathematics, Barnard College, Columbia University, New York, NY, 10027, U.S.A. |
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Abstract: | A Coxeter group is rigid if it cannot be defined by two nonisomorphic diagrams. There have been a number of recent results showing that various classes of Coxeter groups are rigid, and a particularly interesting example of a nonrigid Coxeter group has been given by Bernhard Mühlherr. We show that this example belongs to a general operation of diagram twisting . We show that the Coxeter groups defined by twisted diagrams are isomorphic, and, moreover, that the Artin groups they define are also isomorphic, thus answering a question posed by Charney. Finally, we show a number of Coxeter groups are reflection rigid once twisting is taken into account. |
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Keywords: | Coxeter groups Artin groups diagram twisting rigidity |
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