I could use some help on the Virasoro Algebra and how it relates to conformal field theory. My Algebra skills are pretty elementary so if there's any way to have mercy on me and describe it simply (if possible) I ask that you do so.

As there may be different extensions the Virasoro Algebra I'm working with is defined in terms of L_n:

$\displaystyle \[ L_m, L_n \] = (m - n) L_{m + n} + \frac{c}{12} (m^3 - m) \delta _{m + n, 0}$

$\displaystyle \[ L_m, c \] = 0$

where c is the central charge.