Planar Algebra of the Subgroup-Subfactor
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 $.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2008
- DOI:
- 10.48550/arXiv.0806.1791
- arXiv:
- arXiv:0806.1791
- Bibcode:
- 2008arXiv0806.1791G
- Keywords:
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- Mathematics - Operator Algebras;
- 46L37
- E-Print:
- 30 pages