Planar Algebra of the Subgroup-Subfactor
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2008
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| _version_ | 1866912795388280832 |
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| author | Gupta, Ved Prakash |
| author_facet | Gupta, Ved Prakash |
| contents | 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 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0806_1791 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Planar Algebra of the Subgroup-Subfactor Gupta, Ved Prakash Operator Algebras 46L37 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 $. |
| title | Planar Algebra of the Subgroup-Subfactor |
| topic | Operator Algebras 46L37 |
| url | https://arxiv.org/abs/0806.1791 |