Commutator formulas in groups of Kac-Moody type
Williams, Robert, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Abramenko, Peter, AS-Mathematics, University of Virginia
In this thesis, I prove that root groups associated to nested roots in certain rank 3 hyperbolic buildings must commute. Also, I give necessary and sufficient conditions for existence of nontrivial commutators between root groups associated to roots generating infinite root systems in Kac-Moody groups. Lastly, a gap in the literature regarding “reduction to rank 2” in Kac-Moody root systems is filled.
PHD (Doctor of Philosophy)
Kac-Moody groups, groups of Kac-Moody type, commutator formulas, algebra, buildings, group actions, Moufang, Morita