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.

Details

Original languageEnglish
Number of pages42
JournalIsrael Journal of Mathematics
Early online date28 Dec 2018
Publication statusE-pub ahead of print - 28 Dec 2018