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    • Planar Algebra of the Subgroup-Subfactor

      Ved Prakash Gupta

      Volume 118 Issue 4 November 2008 pp 583-612

    • Fulltext

       

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      Permanent link:
      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

       

      Ved Prakash Gupta1

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

    • Dates

       
      Published
      November 2008
      Manuscript received
      5 September 2007

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