On the Structure of Modular Categories
| dc.creator | Mueger, Michael | |
| dc.date | 2002-01-03 | |
| dc.date.accessioned | 2026-07-07T04:45:39Z | |
| dc.date.available | 2026-07-07T04:45:39Z | |
| dc.description | For a braided tensor category C and a subcategory K there is a notion of centralizer C_C(K), which is a full tensor subcategory of C. A pre-modular tensor category is known to be modular in the sense of Turaev iff the center Z_2(C):=C_C(C) (not to be confused with the center Z_1 of a tensor category, related to the quantum double) is trivial, i.e. equivalent to Vect, and dim(C)<>0. Here dim(C)=sum_i d(X_i)^2, the X_i being the simple objects. We prove the following double centralizer theorem: Let C be a modular category and K a full tensor subcategory closed w.r.t. direct sums, subobjects and duals. Then C_C(C_C(K))=K and dim(K)dim(C_C(K))=dim(C). We give several applications, the most important being the following. If C is modular and K is a full modular subcategory, then also L=C_C(K) is modular and C is equivalent as a ribbon category to the direct product of K and L. Thus every modular category factorizes (non-uniquely, in general) into prime ones. We study the prime factorizations of the categories D(G)-Mod, where G is a finite abelian group. | |
| dc.description | 19 pages, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/math/0201017 | |
| dc.identifier | http://arxiv.org/abs/math/0201017 | |
| dc.identifier | Proc. Lond. Math. Soc. 87 (2003) 291-308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63033 | |
| dc.subject | Category Theory | |
| dc.subject | 18D10; 57M27 | |
| dc.title | On the Structure of Modular Categories | |
| dc.type | text |