Hello, how does one solve these questions?

2. Show that the adjoint representation and the standard representation are isomorphic representations of the Lie algebra so(3). Show that the adjoint and standard representations of the group SO(3) are isomorphic. 3. Using the commutation relation [F(X), A(Y)] = n(H) and induction on k, verify the relation (4.15). 4. Define a vector space with basis uo, u1, ... , Um. Now, define operators A (H), n(X), and A(Y) by formula (4.16). Verify by direct computation that the oper- ators defined by (4.16) satisfy the commutation relations (4.11) for sl(2; C). Hint: When dealing with A(Y), treat the case of uk, k