|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Galois Theory for Braided Tensor Categories and the Modular Closure | | Michael Mueger
; | | Date: |
7 Dec 1998 | | Journal: | Adv. Math. 150, 151-201 (2000) | | Subject: | Category Theory | math.CT hep-th | | Abstract: | 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
times 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
times S and closed subgroups of the Galois group Gal(C
times S/C)=Aut_C(C
times S) of C, the latter being isomorphic to the compact group associated to S by the duality theorem of Doplicher and Roberts. Denoting by Dsubset 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
times S iff Ssubset D. Under this condition C
times 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
times 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
times S can be clarified quite explicitly in terms of group cohomology. | | Source: | arXiv, math.CT/9812040 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER