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Results tagged with planar-algebras
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user 57468
3
votes
Accepted
Generalization of the product formula on subfactors
There are various ways to generalize the equation. I give two different ones here:
(1) In terms of bimodules: Take a finite index irreducible subfactor $N \subset M$. Suppose $P_1$ and $P_2$ are two …
- 146
5
votes
Accepted
What's the relation between fusion and coproduct?
In the formula, $tr(b)$ should be replaced by $tr(|b|)$, i.e., $\|b\|_1$.
$$b_\alpha*b_\beta=\sum_\gamma\frac{\|b_\alpha\|_1\|b_\beta\|_1\bar{c}_{\alpha\beta}^\gamma}{\sqrt{n}\|b_\gamma\|_1}b_\gamma …
- 146
2
votes
Accepted
Existence of a third intermediate if there are two intermediate subfactors of index 2
The answer is yes. Moreover, $K_1\cap K_2 \subset M$ is a dihedral group subfactor, so the lattice of intermediate subfactors between $K_1 \cap K_2$ and $M$ is clear.
Proof: Let us look at the dual …
- 146