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Results tagged with qa.quantum-algebra
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user 184
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
38
votes
4
answers
5k
views
Invertible matrices of natural numbers are permutations... why?
I have heard the following statement several times and I suspect that there is an easy and elegant proof of this fact which I am just not seeing.
Question: Why is it true that an invertible nxn …
- 27.5k
23
votes
5
answers
3k
views
Do all 3D TQFTs come from Reshetikhin-Turaev?
The Reshetikhin-Turaev construction take as input a Modular Tensor Category (MTC) and spits out a 3D TQFT. I've been told that the other main construction of 3D TQFTs, the Turaev-Viro State sum constr …
- 27.5k
13
votes
Why are fusion categories interesting?
I also wrote a sequence of blog posts explaining the Turaev-Viro construction from the point of view of planar algebras. It has pretty pictures and might be relevant.
TQFTs via Planar Algebras I
TQF …
12
votes
1
answer
602
views
A linear category with objects of infinite length but which is otherwise finite?
Fix a ground field $k$. By a linear category I will mean an Abelian category which is compatibly enriched over $k$-vector spaces. A linear category is called finite if it satisfies the following four …
- 27.5k
12
votes
Accepted
How unique are extensions of TQFTs to lower dimension?
The question of which tqfts extend is a very interesting one. To make the question more mathematically precise, we can fix the target n-categories and ask for the tqfts to extend with respect to those …
- 27.5k
11
votes
0
answers
412
views
When can we tell if PROPs, Algebraic Theories, etc. are faithfully detected in a given categ...
I am interested in understanding a certain phenomenon. I am hoping this sort of problem has been studied before, but I don't know the proper terminology and am having trouble finding answers. I am goi …
- 27.5k
9
votes
2
answers
444
views
How weird can Modular Tensor Categories be over non-algebraically closed fields?
I am trying to understand better the behaviour and character of modular tensor categories over non-algebraically closed fields. How weird can they be?
The reason I am interested in this is that my co …
- 27.5k
7
votes
Accepted
Are the “identity object axioms” in the definition of a braided monoidal category needed? (A...
This is Proposition 1 in the seminal paper "Braided Monoidal Categories" by Joyal and Street. Relation (ii) is implied by the others.
- 27.5k
6
votes
TQFT and Mapping Class Groups
The following paper answers your question precisely, I think: arxiv:1408.0668
Specifically Theorem 1.3 (which is elaborated on in Section 4) describes precisely what additional data you must specify …
- 27.5k
6
votes
1
answer
167
views
Commutative Frobenius algebra with non-invertible window element, but not square zero
For any commutative Frobenius algebra $A$ there is an associated window element $\omega \in A$. If $\mu: A \otimes A \to A$ denotes the multiplication, $1 \in A$ the unit, $b: A \otimes A \to k$ the n …
- 27.5k
5
votes
Drinfeld center of a Deligne tensor product
Here is another way to see this. As noticed by Theo in the comments to the OP, the center of $\mathcal{E}$ is the endomorphism category of $\mathcal{E}$ as and $\mathcal{E}$-$\mathcal{E}$-bimodule cat …
- 27.5k