1. The extension should definitely be unique because the whole theory can be computed from the value of the point.

@KevinCarlson: Ohhh yeah, obviously! Thanks for pointing that out.

this is a really great question. A related question, which I am going pose with absolutely no explanation: Is the trace of the T-matrix for the Drinfeld center of a unitary fusion category always real? I just spent the past hour computing and it seems like the answer might be yes....

further down on the page there is a link to which has more information en.wikipedia.org/wiki/…

If you can find a vector field $X$ on a neighborhood U such that $[X,JX]=0$ on $U$, then that neighborhood is isomorphic to $\mathbb{C}$. This is because the Lie bracket is the obstruction to $X,JX$ "integrating" to a coordinate grid

i am generating random elements like this: (x1/100,x2/100,...) where x1,x2,... are indipendently sampled from between 1 and 100

yeah it doesn't work once d is too big, but i just did a d=4

i just implemented it. Everything is good :D

It still works really nicely. I have been using the same trick for commutative algebras for ages, it just never occurred to me that it generalized

That makes sooooo much sense. Thank you very much :D