Galois Theory for Braided Tensor Categories and the Modular Closure
| dc.creator | Mueger, Michael | |
| dc.date | 1998-12-07 | |
| dc.date | 1999-10-05 | |
| dc.date.accessioned | 2026-07-07T05:27:08Z | |
| dc.date.available | 2026-07-07T05:27:08Z | |
| dc.description | Given a braided tensor *-category C with conjugate (dual) objects and irreducible unit together with a full symmetric subcategory S we define a crossed product C\rtimes S. This construction yields a tensor *-category with conjugates and an irreducible unit. (A *-category is a category enriched over Vect_C with positive *-operation.) A Galois correspondence is established between intermediate categories sitting between C and C\rtimes S and closed subgroups of the Galois group Gal(C\rtimes S/C)=Aut_C(C\rtimes S) of C, the latter being isomorphic to the compact group associated to S by the duality theorem of Doplicher and Roberts. Denoting by D\subset C the full subcategory of degenerate objects, i.e. objects which have trivial monodromy with all objects of C, the braiding of C extends to a braiding of C\rtimes S iff S\subset D. Under this condition C\rtimes S has no degenerate objects iff S=D. If the original category C is rational (i.e. has only finitely many equivalence classes of irreducible objects) then the same holds for the new one. The category C\rtimes D is called the modular closure of C since in the rational case it is modular, i.e. gives rise to a unitary representation of the modular group SL(2,Z). (In passing we prove that every braided tensor *-category with conjugates automatically is a ribbon category, i.e. has a twist.) If all simple objects of S have dimension one the structure of the category C\rtimes S can be clarified quite explicitly in terms of group cohomology. | |
| dc.description | latex2e, 39 pages. Style file included via filecontents command. Final version, to appear in Adv. Math. Purely notational improvements | |
| dc.identifier | https://arxiv.org/abs/math/9812040 | |
| dc.identifier | http://arxiv.org/abs/math/9812040 | |
| dc.identifier | Adv. Math. 150, 151-201 (2000) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77811 | |
| dc.subject | Category Theory | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Galois Theory for Braided Tensor Categories and the Modular Closure | |
| dc.type | text |