Lie algebras generated by reflections in types BCD
arXiv:2506.01198 · doi:10.1016/j.jpaa.2026.108278
Abstract
We consider the group algebra over the field of complex numbers of the Weyl group of type B (the hyperoctahedral group, or the group of signed permutations) and of the Weyl group of type D (the demihyperoctahedral group, or the group of even-signed permutations), viewed as Lie algebras via the commutator bracket, and determine the structure of the Lie subalgebras generated by the sets of reflections.
41 pages. Version 2 has various expositional improvements and minor corrections. We have also included a supplementary file containing GAP code for computing the Lie algebra generated by reflections. Download the source files to find a text file containing the code