Lie algebras generated by reflections in types BCD
Representation Theory
2026-05-06 v2
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.
Cite
@article{arxiv.2506.01198,
title = {Lie algebras generated by reflections in types BCD},
author = {Christopher M. Drupieski and Jonathan R. Kujawa},
journal= {arXiv preprint arXiv:2506.01198},
year = {2026}
}
Comments
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