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Singly generated planar algebras of small dimension, Part III

Dietmar Bisch Department of Mathematics, Vanderbilt University, Nashville TN 37235 Vaughan F. R. Jones Department of Mathematics, Vanderbilt University, Nashville TN 37235 Zhengwei Liu Department of Mathematics, Vanderbilt University, Nashville TN 37235

Quantum Algebra Spectral Theory and Operator Algebra mathscidoc:2206.29004

Transactions of the American Mathematical Society, 369, (4), 2461–2476, 2016.7
The first two authors classified subfactor planar algebra generated by a non-trivial 2-box subject to the condition that the dimension of 3-boxes is at most 12 in Part I; 13 in Part II of this series. They are the group planar algebra for , the Fuss-Catalan planar algebra, and the group/subgroup planar algebra for Z_2 ⊂ Z_5 \rtimes Z_2.. In the present paper, we extend the classification to 14 dimensional 3-boxes. They are all Birman-Murakami-Wenzl algebras. Precisely it contains a depth 3 one from quantum O(3), and a one-parameter family from quantum S_p(4).
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@inproceedings{dietmar2016singly,
  title={Singly generated planar algebras of small dimension, Part III},
  author={Dietmar Bisch, Vaughan F. R. Jones, and Zhengwei Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626172625507839478},
  booktitle={Transactions of the American Mathematical Society},
  volume={369},
  number={4},
  pages={2461–2476},
  year={2016},
}
Dietmar Bisch, Vaughan F. R. Jones, and Zhengwei Liu. Singly generated planar algebras of small dimension, Part III. 2016. Vol. 369. In Transactions of the American Mathematical Society. pp.2461–2476. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626172625507839478.
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