Reflection systems and partial root systems
We develop a general theory of reflection systems and, more
specifically, partial root systems which provide a unifying framework for
finite root systems, Kac-Moody root systems, extended affine root systems and
various generalizations thereof. Nilpotent and prenilpotent subsets are
studied in this setting, based on commutator sets and the descending central
series. We show that our notion of a prenilpotent pair coincides, for
Kac-Moody root systems, with the one defined by Tits in terms of positive
systems and the Weyl group.
(Updated version 1 March 2007)
(This paper has appeared in Forum Math. 23 (2011), 349--411)
O. Loos < ottmar.loos@uibk.ac.at >
E. Neher < neher@uottawa.ca >