- #1
pdxautodidact
- 26
- 0
Homework Statement
Use the Jacobi identity in the form
$$ \left[e_i, \left[e_j,e_k\right]\right] + \left[e_j, \left[e_k,e_i\right]\right] + \left[e_k, \left[e_i,e_j\right]\right] $$
and ## \left[e_i,e_j\right] = c^k_{ij}e_k ## to show that the structure constants ## c^k_{ij} ## satisfy the identity
$$ c^h_{im}c^m_{jk} + c^h_{km}c^m_{ij} + c^h_{jm}c^m_{ki} = 0 $$
Homework Equations
The Attempt at a Solution
Not sure where to start with this one. Using the definition of the structure constant I can show the Jacobi identity equals zero, but does this imply the structure constant identity is equal to zero? I don't see it, if so. Anyway, still not homework, I'm doing this stuff by myself. Also, Einstein convention is enforced (as always).
Any advice for this would be better than the solution, I just started working on it today and moved on so I could sleep on it.
cheers.