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Classification of Curtis–Tits and Phan amalgams with 3-spherical diagram

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Abstract

We classify all non-collapsing Curtis–Tits and Phan amalgams with 3- spherical diagram over all fields. In particular, we show that amalgams with spherical diagram are unique, a result required by the classification of finite simple groups. We give a simple condition on the amalgam which is necessary and sufficient for it to arise from a group of Kac–Moody type. This also yields a definition of a large class of groups of Kac–Moody type in terms of a finite presentation.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA

    Rieuwert J. Blok

  2. School of Mathematics, University of Birmingham, Edgbaston, B15 2TT, UK

    Rieuwert J. Blok, Corneliu G. Hoffman & Sergey V. Shpectorov

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  1. Rieuwert J. Blok
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  2. Corneliu G. Hoffman
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  3. Sergey V. Shpectorov
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Correspondence to Rieuwert J. Blok.

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Blok, R.J., Hoffman, C.G. & Shpectorov, S.V. Classification of Curtis–Tits and Phan amalgams with 3-spherical diagram. Isr. J. Math. 230, 97–140 (2019). https://doi.org/10.1007/s11856-018-1819-5

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  • DOI: https://doi.org/10.1007/s11856-018-1819-5

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