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Group-type subfactors and Hadamard matrices | | Richard D. Burstein
; | | Date: |
8 Nov 2008 | | Abstract: | A hyperfinite $II_1$ subfactor may be obtained from a symmetric commuting
square via iteration of the basic construction. For certain commuting squares
constructed from Hadamard matrices, we describe this subfactor as a group-type
inclusion $R^H subset R
times K$, where $H$ and $K$ are finite groups with
outer actions on the hyperfinite $II_1$ factor $R$. We find the group of outer
automorphisms generated by $H$ and $K$, and use the method of Bisch and
Haagerup to determine the principal and dual principal graphs. In some cases a
complete classification is obtained by examining the element of $H^3(H ast K /
Int R)$ associated with the action. | | Source: | arXiv, 0811.1265 | | Services: | Forum | Review | PDF | Favorites | |
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