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 < >

E. Neher < >