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Lie algebras generated by reflections in types BCD
Christopher M. Drupieski, Jonathan R. Kujawa
https://arxiv.org/abs/2506.01198 https://

Lie algebras generated by reflections in types BCD
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.