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Apr
13
comment Definition of a cosemisimple Hopf algebra
It sounds like you may want to go back and read a book on finite dimensional representations of finite groups (I like the first 2/3rds of Serre or Teleman's online notes) before tackling Hopf algebras.
Apr
13
comment Definition of a cosemisimple Hopf algebra
Seems fine to me (at least for coalgebras, maybe the Hopf structure gives some additional constraints).
Apr
13
revised Definition of a cosemisimple Hopf algebra
deleted 145 characters in body
Apr
13
answered Definition of a cosemisimple Hopf algebra
Mar
23
comment Artin reciprocity $\implies $ Cubic reciprocity
At any rate, I certainly can't vouch for whether my 21 year old self knew how to deal with this issue. My guess is I overlooked this point.
Mar
23
comment Artin reciprocity $\implies $ Cubic reciprocity
I read this question and thought it was a nice question, and was wondering to myself whether this argument something I knew back in the day... And then I was a bit startled when I clicked through the link.
Mar
22
awarded  Popular Question
Mar
17
awarded  Enlightened
Mar
17
awarded  Nice Answer
Mar
12
accepted Technical issue in the approach to Lie groups taken in a book
Mar
9
answered When modular tensor categories are equivalent?
Mar
7
comment Why should affine lie algebras and quantum groups have equivalent representation theories?
Yeah, you're right, I was oversimplifying a little. Kuperberg's result gets you most of the way there, but you need a bit more to turn it into a full Wenzl-style recognition theorem. Our trivalent paper gets further towards that, but one needs a bit more as discussed in those slides. There's still a few cases from those slides that haven't made it into papers yet, but should soon. At any rate, Kuperberg's paper is enough to suggest that these techniques should be enough for G2 even though he didn't prove precisely this.
Mar
4
comment Why should affine lie algebras and quantum groups have equivalent representation theories?
Kuperberg proved a result like this for G2. But the larger exceptionals are beyond the range of current techniques.
Feb
10
awarded  Good Question
Feb
4
comment Can the ribbon category of f.d. reps of $\mathcal{U}_q(\mathfrak{sl}(2))$ be modified so the twist is trivial on the vector representation?
The point here is roughly that central character gives a grading on representations, and so elements of the center of the corresponding Lie group give you the ways of changing ribbon structure. For SL the center is finite and so you only get a few ribbon structures, but for GL the center is the scalars and so you can change ribbon structure at the vector rep however you want. The ribbon structure won't be trivial everywhere, in particular the quantum determinant will no longer have trivial ribbon element (which is why this ribbon structure doesn't descend to SL).
Jan
29
awarded  gr.group-theory
Jan
28
revised Technical issue in the approach to Lie groups taken in a book
added 11 characters in body
Jan
28
answered Technical issue in the approach to Lie groups taken in a book
Jan
28
comment Technical issue in the approach to Lie groups taken in a book
@TheoJohnson-Freyd: Thanks! It was just a bit weird that I kept finding that same detail skipped over and over again when trying to look this up.
Jan
27
answered Technical issue in the approach to Lie groups taken in a book