It's ultimately your call, but I'd wait a bit. IMO opinion there is no urgency - whether the tag is created today or a week later, there's not much of a difference.

From the downvote I gather that at least one user has some objections to the new tag. So maybe leaving a few days to see whether somebody explains in the comments why they see a problem with the tag would be reasonable.

On the contrary, there's no such tag about "semisimple-***" in MO.

And another question, should MSE share the same tag management as MO as possible?

@Andrews Well, to this there is a simple answer - definitely not. (At least, several aspects are not suitable for MSE.)

One thing is that on MO people pay much less attention to managing tags. (Although I might be biased here.)

But one thing that would be difficult on Mathematics is that MO requires each question to have one of the "arXiv" tags (top-level tags). See, for example: Why are MO tags formatted as they are? and Frequently asked questions about tagging on MathOverflow

This was discussed a bit also on our meta: Should MathOverflow tag prefixes be used? and Should math.SE have top level tags?.

And also if you look at some specific tags, there are differences. For example abstract-algebra, discrete-mathematics and geometry are deprecated on MathOverflow. (Which means that they shouldn't be used and the tags should eventually be removed completely.)

On Mathematics, the tags with the same names are commonly used, in fact, they are among the largest tags: abstract-algebra, geometry, discrete-mathematics.

Another example is calculus. This tag has been already removed on MathOverflow. I think that the discussion which lead to deprecating this tag on MO was this one: Tags that encourage off-topic questions.

So if we wanted all of the tags to be same on MO and MSE, it would mean removal of the tags calculus, abstract-algebra, geometry, etc.

@MartinSleziak Yes, I figured it out, lots of tags in MO have no wki (since MO is for mathematicians, it's not a big problem, though). I don't mean MSE should have same tags as MO, just wonder if a tag exist in MO, should it also be created in MSE (like mirror-symmetry before and semisimple-Lie-algebras this time)

Since there's no such tag about "semisimple-Lie-algebras" in MO, I begin to doubt if it's necessary enough to create that tag in MSE now.

If a tag exists on MO, that might be an indication that it's possibly useful. But I would not consider it to be that important criterion.

To be blunt, the site with better tag-system might occasionally learn something from the site where the tag-system is worse - but not always. (Again, I might be biased here.)

I have mentioned above several examples of tags which do not exists on MO, but are perfectly fine on MSE.

It is also the other way round, the tags (ultrafilters) and (stone-cech-compactification) exist on MO, but they were deemed to be too specific when discussed on this site.

@Andrews So perhaps the fact that such tag does not exist on MO is a minor indication that it is not needed here either - but I would not consider this as a very important criterion.

Perhaps you can mention the fact that the tag does not exist on MO as a comment to your post. (Or if you prefer you could edit it directly into the post to make it more visible.)

So that the people who join the discussion about the new tag on meta see this.

@Andrews that a tag exists on MO might not be a good indicator that MSE should have, IMO. Since there are so many questions nowadays, people (well, at least me) uses tags in an essential way to local their questions (MO don't have this problem). So if a tag is too specific, it runs into the problem that people might miss the question.

e.g. For a standard question say Lagrangian floer homology, one could easily uses all the tags: Fukata Category, A-\infinty algebra, Floer homology (these tags exists in MO but not in here). this would be a problem if all these tags exists in MSE: since they occurs rarely, people in the fields will not follow that daily. So if a post uses only one of the above tags, then likely some users interested in the post missed that.

So in some cases it would be better, IMO, to make a general tags which basically covers most of the related problem (for advanced topics).

I thought about this point when you suggested "mirror symmetry" on meta, but I cannot think of a more general tags in that moment.