Lets say that we know the value of the commutators [A,B] and [A,C]. Is there any way so that we can calculate value of commutator [B,C]? I looked up various sources for commutator identities, but somehow all of them fail to solve this.
2026-03-29 08:44:53.1774773893
Commutator Algebra
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If $A$ is in the centre of the group/Lie algebra (I don't know what the context is), then the first two commutators are trivial, while the third can be anything.