Talk:Special linear Lie algebra

Please elaborate
Under the section Representation theory of $$\mathfrak{sl}_2 \mathbb C$$, this sentence appears:

"Note that, here, the powers $$f^k$$, etc. refer to powers as elements of the algebra U and not matrix powers."

I do not understand what kind of "powers" this refers to, since the only powers that I know of in a Lie algebra are brackets of an element with itself, and these are always 0. So it would be a good idea if someone knowledgeable about this subject explained what this means in the article. 2601:200:C000:1A0:A960:2026:2D93:BC3A (talk) 15:02, 18 September 2021 (UTC)