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

  • Rieuwert J. BlokEmail author
  • Corneliu G. Hoffman
  • Sergey V. Shpectorov
Article

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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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • Rieuwert J. Blok
    • 1
    • 2
    Email author
  • Corneliu G. Hoffman
    • 2
  • Sergey V. Shpectorov
    • 2
  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA
  2. 2.School of MathematicsUniversity of BirminghamEdgbastonUK

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