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- W2060804904 abstract "Coxeter groups have presentations $langle S :(st)^{m_{st}}forall s,tin S rangle$ where for all $s,tin S$, $m_{st}in {1,2,ldots ,infty }$, $m_{st}=m_{ts}$ and $m_{st}=1$ if and only if $s=t$. A fundamental question in the theory of Coxeter groups is: Given two such âCoxeter presentations, do they present the same group? There are two known ways to change a Coxeter presentation, generally referred to as twisting and simplex exchange. We solve the isomorphism question for Coxeter groups with an even Coxeter presentation (one in which $m_{st}$ is even or $infty$ when $sne t$). More specifically, we give an algorithm that describes a sequence of twists and triangle-edge exchanges that either converts an arbitrary finitely generated Coxeter presentation into a unique even presentation or identifies the group as a non-even Coxeter group. Our technique can be used to produce all Coxeter presentations for a given even Coxeter group." @default.
- W2060804904 created "2016-06-24" @default.
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- W2060804904 date "2007-09-01" @default.
- W2060804904 modified "2023-10-16" @default.
- W2060804904 title "The even isomorphism theorem for Coxeter groups" @default.
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- W2060804904 doi "https://doi.org/10.1090/s0002-9947-07-04133-5" @default.
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