• Planar Algebra of the Subgroup-Subfactor

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/118/04/0583-0612

• # Keywords

Planar algebras; subfactors; standard invariant.

• # Abstract

We give an identification between the planar algebra of the subgroup-subfactor $R \rtimes H \subset R \rtimes G$ and the 𝐺-invariant planar subalgebra of the planar algebra of the bipartite graph $\star_n$, where $n=[G:H]$. The crucial step in this identification is an exhibition of a model for the basic construction tower, and thereafter of the standard invariant of $R \rtimes H \subset R \rtimes G$ in terms of operator matrices.

We also obtain an identification between the planar algebra of the fixed algebra subfactor $R^G \subset R^H$ and the 𝐺-invariant planar subalgebra of the planar algebra of the `flip’ of $\star_n$.

• # Author Affiliations

1. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India

• # Proceedings – Mathematical Sciences

Volume 130, 2020
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Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019