This may well be something of a silly question, but if so, then all the more reason I get it straightened out.
I have in the past been working with representations of both groups and algebras, and in the literature I've been using, the traces of the representation matrices of both have always been referred to as characters of the representation.
Now, I'm looking properly into Lie algebras for the first time since far too long ago, and I come across a note that says that the weight of a representation of an algebra is the analogue of the character of a representation of a group.
Are weights of representations of algebras and characters of representations of algebras then the very same thing, and its just that people who work in associative algebra and people who work with Lie algebras uses differing terminology, or is there something of much importance that I am missing here?
Much look forward to getting this sorted out!