![SOLVED: (b) Show that LL=0 Hint: The following commutator identities are helpful: [B,A]=-[A,B] [A,A]=0 [A,B+C]=[A,B]+[A,C] [A+B,C]=[A,C]+[B,C] [A,BC]=[A,B]C+B[A,C] [AB,C]=[A,C]B+A[B,C] [AB,CD]=[A,C]BD+A[B,C]D+C[A,D]B+AC[B,D] SOLVED: (b) Show that LL=0 Hint: The following commutator identities are helpful: [B,A]=-[A,B] [A,A]=0 [A,B+C]=[A,B]+[A,C] [A+B,C]=[A,C]+[B,C] [A,BC]=[A,B]C+B[A,C] [AB,C]=[A,C]B+A[B,C] [AB,CD]=[A,C]BD+A[B,C]D+C[A,D]B+AC[B,D]](https://cdn.numerade.com/ask_images/08590acd058a4573a39efba56c340cc5.jpg)
SOLVED: (b) Show that LL=0 Hint: The following commutator identities are helpful: [B,A]=-[A,B] [A,A]=0 [A,B+C]=[A,B]+[A,C] [A+B,C]=[A,C]+[B,C] [A,BC]=[A,B]C+B[A,C] [AB,C]=[A,C]B+A[B,C] [AB,CD]=[A,C]BD+A[B,C]D+C[A,D]B+AC[B,D]
![SOLVED: Commutators: (a) Prove the following identities: [A, [B, C]] + [B, [C, A]] + [C, [A, B]] = 0 (A, B) = [B, A] (1) (2) (b) The commutator between two SOLVED: Commutators: (a) Prove the following identities: [A, [B, C]] + [B, [C, A]] + [C, [A, B]] = 0 (A, B) = [B, A] (1) (2) (b) The commutator between two](https://cdn.numerade.com/ask_images/1b69a13aefe24d5f8637431d6fec1d04.jpg)
SOLVED: Commutators: (a) Prove the following identities: [A, [B, C]] + [B, [C, A]] + [C, [A, B]] = 0 (A, B) = [B, A] (1) (2) (b) The commutator between two
![PDF) Commutator identities on associative algebras and the integrability of nonlinear evolution equations PDF) Commutator identities on associative algebras and the integrability of nonlinear evolution equations](https://i1.rgstatic.net/publication/227148191_Commutator_identities_on_associative_algebras_and_the_integrability_of_nonlinear_evolution_equations/links/09e4150f94190e807d000000/largepreview.png)
PDF) Commutator identities on associative algebras and the integrability of nonlinear evolution equations
![SOLVED: Prove the following commutator identities: [A, B] = [A, B] + [B, A] [AB, C] = A[B, C] + [A, C]B SOLVED: Prove the following commutator identities: [A, B] = [A, B] + [B, A] [AB, C] = A[B, C] + [A, C]B](https://cdn.numerade.com/ask_images/8b6b6345b5484bfd9ee39eb10255d3e3.jpg)