# ON THE PLANAR ALGEBRA OF OCNEANU'S ASYMPTOTIC INCLUSION

@article{Curran2012ONTP, title={ON THE PLANAR ALGEBRA OF OCNEANU'S ASYMPTOTIC INCLUSION}, author={Stephen J. Curran}, journal={International Journal of Mathematics}, year={2012}, volume={23}, pages={1250114} }

In recent joint work with Jones and Shlyakhtenko, we have given a diagrammatic description of Popa's symmetric enveloping inclusion for planar algebra subfactors. In this paper, we give a diagrammatic construction of the associated Jones tower, in the case that the planar algebra is finite-depth. We then use this construction to describe the planar algebra of the symmetric enveloping inclusion, which is known to be isomorphic to the planar algebra of Ocneanu's asymptotic inclusion by a result…

## 4 Citations

### Title Cohomology and L-2-Betti Numbers for Subfactors and QuasiRegular Inclusions Permalink

- Mathematics
- 2015

We introduce L-Betti numbers, as well as a general homology and cohomology theory for the standard invariants of subfactors, through the associated quasi-regular symmetric enveloping inclusion of II1…

### Drinfeld center of planar algebra

- Mathematics
- 2012

We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra $P$ (not necessarily having finite depth). We prove that if $N \subset M$ is a…

### O A ] 2 3 N ov 2 01 5 Cohomology and L 2-Betti numbers for subfactors and quasiregular inclusions

- Mathematics
- 2015

We introduce L-Betti numbers, as well as a general homology and cohomology theory for the standard invariants of subfactors, through the associated quasi-regular symmetric enveloping inclusion of II1…

### Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions

- Mathematics
- 2015

We introduce $L^2$-Betti numbers, as well as a general homology and cohomology theory for the standard invariants of subfactors, through the associated quasi-regular symmetric enveloping inclusion of…

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