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comment An elegant description for graded-module morphisms with non-zero zero component
Well, I don't remember. I do remember that I was localizing by these morphisms and that was what I meant by quotienting. Judging by the date, I was probably trying to work out a ncag example. I don't have a clue what it was!
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comment Why do we use the commutator bracket for Lie algebra's
Yes, B R this is also a nice point. Although somehow that seems to depend on some of the other facts. In particular, we define Lie alg reps to be compatible with the structure, which is the Jacobi identity...