5
votes
Accepted
Backwards stable factors
For $\textrm{II}_1$ factors, your definitions of backwards stable and stable are the same. The point here is that for a $\textrm{II}_1$ factor $R$ you can talk about $M_n(R)$ for all positive number $...
- 1,262
4
votes
Some fusion rings/categories I don't recognize
These fusion categories are all weakly integral, each with an FPdim less than 84, and therefore, they are all weakly group-theoretical by this paper. Consequently, they can all be described using ...
3
votes
Non-cyclotomic modular fusion categories
A detailed discussion of your question can be found in Davidovitch et. al's paper "On arithmetic modular tensor categories". They say that it is still an open problem whether there are non-...
- 2,817
2
votes
Unitary structures on fusion categories
Reutter's recent paper "uniqueness of unitary structure for unitarizable fusion categories" answers your question in the affirmative (link: https://arxiv.org/pdf/1906.09710.pdf).
- 2,817
1
vote
Accepted
Intersection of two intermediate subalgebras
The following proof is due to Professor Watatani (through private communication). We sincerely thank him for kindly allowing us to present the proof here.
On contrary assume that $e_\mathscr{C}\wedge ...
- 383
1
vote
Accepted
Relation between factor condition on von Neumann algebras and modularity condition on ribbon fusion categories
Disclaimer: This is a long-winded attempt to answer the "... Are these guises of the same phenomenon?" part of the question. I do not understand how to translate between the two.
There is ...
- 511
1
vote
Accepted
Cyclic vectors and subfactor inlcusion
No. Let $N$ be any $\rm II_1$ factor, and let $\alpha: G\to \operatorname{Aut}(N)$ be an outer action. Then $M:= N\rtimes_\alpha G$ is again a $\rm II_1$ factor, and $N\subset M$ is irreducible, i.e., ...
- 5,335
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