Classification of Curtis–Tits and Phan amalgams with 3-spherical diagram
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.
Unable to display preview. Download preview PDF.
- C. D. Bennett and S. Shpectorov, A new proof of a theorem of Phan, Journal of Group Theory 7 (2004), 287–310.Google Scholar
- R. J. Blok and C. Hoffman, A classfication of Curtis–Tits amalgams, in Groups of Exceptional Type, Coxeter Groups and Related Geometries, Springer Proceedings in Mathematics & Statistics, Vol. 82, Springer, New Delhi, 2014, pp. 1–26.Google Scholar
- J. Dunlap, Uniqueness of Curtis–Phan–Tits amalgams, PhD thesis, Bowling Green State University, 2005.Google Scholar
- R. Gramlich, C. Hoffman and S. Shpectorov, A Phan-type theorem for Sp(2n, q), Journal of Algebra 264 (2003), 358–384.Google Scholar
- K.-W. Phan, A characterization of the unitary groups PSU(4, q2), q odd, Journal of Algebra 17 (1971), 132–148.Google Scholar
- R. A. Wilson, The Finite Simple Groups, Graduate Texts in Mathematics, Vol. 251, Springer, London, 2009.Google Scholar