Online Archive of University of Virginia Scholarship
Commutator formulas in groups of Kac-Moody type250 views
Author
Williams, Robert, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Advisors
Abramenko, Peter, AS-Mathematics, University of Virginia
Abstract
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.
Degree
PHD (Doctor of Philosophy)
Keywords
Kac-Moody groups; groups of Kac-Moody type; commutator formulas; algebra; buildings; group actions; Moufang; Morita
Williams, Robert. Commutator formulas in groups of Kac-Moody type. University of Virginia, Mathematics - Graduate School of Arts and Sciences, PHD (Doctor of Philosophy), 2022-07-28, https://doi.org/10.18130/t9v1-vz61.
