Imaginary roots of a Kac-Moody Lie algebra whose reflections preserve root multiplicities
In contrast with finite dimensional semisimple Lie algebras, the infinite dimensional Kac-Moody Lie algebras possess some roots which are not conjugate to the simple roots under the associated Weyl group. These are the so-called imaginary roots. An imaginary root \(\alpha\) is said to be special if the corresponding reflection \(r_ \alpha\) preserves the root lattice, as well as the sets of real and imaginary roots. These special imaginary roots play an interesting role in the study of generalized spherical buildings. In this paper, the author has provided a complete classification of special imaginary roots for symmetrizable Kac-Moody Lie algebras.
infinite dimensional Kac-Moody Lie algebras
scientific article; zbMATH DE number 218579