Prove commutation relation of galilei boosts and rotations

[ma18]

Homework Statement

Use the formulas given (which have been solved in previous questions) prove that

where w_12 is a complex constant.

From here, induce that

where eps_abc is the fully anti-symmetric symbol

Homework Equations

The equations given to use are:

The Attempt at a Solution

[/B]
First, I expanded the commutator given (cannot give here as I have reached max file upload for a single post), but after that I keep on looking at it and I'm not exactly sure how to proceed. I have proved the first and last of the "relevant equations" and have the expanded forms of that and I think I may have to use that but I am not sure.

Any help would be appreciated.

 

[DrDu]

What do you mean with expanded form?

 

[ma18]

What do you mean with expanded form?

The taylor expansion

 

[DrDu]

From the Taylor expansion of the last equation you gave, the second equation should follow directly given that epsilon is an arbitrary constant.