The Lie subalgebras generated by reflections in the group algebras of Weyl groups of types B and D over ℂ are explicitly described in terms of their isomorphism type and decomposition.
Bourbaki, Lie groups and Lie algebras
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For classical Weyl groups with reflections of odd superdegree, the generated Lie superalgebra equals the derived subalgebra of the group algebra plus the span of the reflection class sums.
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Lie algebras generated by reflections in types BCD
The Lie subalgebras generated by reflections in the group algebras of Weyl groups of types B and D over ℂ are explicitly described in terms of their isomorphism type and decomposition.
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Lie Superalgebras Generated by Reflections in Weyl Groups of Classical Type
For classical Weyl groups with reflections of odd superdegree, the generated Lie superalgebra equals the derived subalgebra of the group algebra plus the span of the reflection class sums.