$C^*$-Tensor Categories in the Theory of $II_1$-Subfactors
| dc.creator | Schaflitzel, R. | |
| dc.date | 1997-01-22 | |
| dc.date.accessioned | 2026-07-07T09:13:41Z | |
| dc.date.available | 2026-07-07T09:13:41Z | |
| dc.description | The article contains a detailed description of the connection between finite depth inclusions of $II_1$-subfactors and finite $C^*$-tensor categories (i.e. $C^*$-tensor categories with dimension function for which the number of equivalence classes of irreducible objects is finite). The $(N,N)$-bimodules belonging to a $II_1$-subfactor $N\subset M$ with finite Jones index form a $C^*$-tensor category with dimension function. Conversely, taking an object of a finite $C^*$-tensor category C we construct a subfactor $A\subset R$ of the hyperfinite $II_1$-factor R with finite index and finite depth. For this subfactor we compute the standard invariant and show that the $C^*$-tensor category of the corresponding $(A,A)$-bimodules is equivalent to a subcategory of C. We illustrate the results for the $C^*$-tensor category of the unitary finite dimensional corepresentations of a finite dimensional Hopf-*-algebra. | |
| dc.description | 58 pages, latex, no figures | |
| dc.identifier | https://arxiv.org/abs/funct-an/9701007 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9701007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152415 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | $C^*$-Tensor Categories in the Theory of $II_1$-Subfactors | |
| dc.type | text |