Envelopping algebra of Lie algebra

[Pape]

Let (L, [ ]) be a Lie algebra and T(L) its tensor algebra. I would like to know why the space
I generated by elements of the form
x *y - y* x - [x, y]
with x and y in L, is a two-sided ideal of the tensor algebra T(L)?

by x*y I mean x tensor y

Thanks!

[Sa Majesté]

Je pense qu'il doit exister pas mal de forums en anglais ...