/sci/ - Science & Math

>>10967211
Yeah, I gotcha.
(The "issue" with that answer is just that he was saying it's a subalgebra of su(2) (which it's not and so that's wrong), but given he was responding to the post constructing a+ib as matrix, it's also clear that he didn't mean that it's a Lie-subalgebra where the algebra operation would be [,]. If x * x isn't 0, then yeah it can't be a Lie-subalgebra of su(2) and that's that, as you say. But if we go back to speaking in terms of the already existing product in a ring over C (of matrices here) and unity I is it, then the c*I represent C. Not very interesting, but just to clarify that there are two notions of "subalgebra" here, as we have two products at hand.)

Incidentally, for people interested in such quotient rings, I did a very light-hearted motivation to universal enveloping algebras yesterday:

https://youtu.be/x_H64Q2GZfw