Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~, B^~] congruent A^~ B^~ - B^~ A^~. Let a, b, ... be constants, then identities include [f(x), x] | = | 0 [A^~, A^~] | = | 0 [A^~, B^~] | = | -[B^~, A^~] [A^~, B^~ C^~] | = | [A^~, B^~]C^~ + B^~[A^~, C^~] [A^~ B^~, C^~] | = | [A^~, C^~]B^~ + A^~[B^~, C^~] [a + A^~, b + B^~] | = | [A^~, B^~] [A^~ + B^~, C^~ + D^~] | = | [A^~, C^~] + [A^~, D^~] + [B^~, C^~] + [B^~, D^~].

adjoint representation | anticommutator | commutator subgroup | Jacobi identities