Reflections of root lattices for Kac-Moody algebras (Q1911780)

The author builds on work of \textit{C. Bennett} [J. Algebra 158, 244-267 (1993; Zbl 0795.17031)] to give a necessary and sufficient condition for a primitive element \(\alpha\) (with \((\alpha, \alpha) \neq 0\)) of the root lattice \(Q\) of a Kac-Moody Lie algebra \(g\) with symmetrizable Cartan matrix) to satisfy \(r_\alpha \Delta= \Delta\) where \(\Delta\) is the root system of \(g\). He also obtains some partial results towards determining which \(\alpha\in Q\) satisfy \(r_\alpha Q=Q\).