On $G$--equivariant modular categories
| dc.creator | Kirillov Jr, Alexander | |
| dc.date | 2004-01-12 | |
| dc.date.accessioned | 2026-07-07T05:04:30Z | |
| dc.date.available | 2026-07-07T05:04:30Z | |
| dc.description | In this paper, we study $G$-equivariant tensor categories for a finite group $G$. These categories were introduced by Turaev under the name of $G$-crossed categories; the motivating example of such a category is the category of twisted modules over a vertex operator algebra $V$ with a finite group of automorphisms $G$. We discuss the notion of "orbifold quotient" of such a category (in the example above, this quotient is the category of modules over the subalgebra of invariants $V^G$). We introduce an extended Verlinde algebra for a $G$-equivariant tensor category and give a simple description of the Verlinde algebra of the orbifold category in terms of the extended Verlinde algebra of the original category. We define an analog of $s,t$ matrices for the extended Verlinde algebra and show that if $s$ is invertible, then these matrices define an action of $SL_2(Z)$ on the extended Verlinde algebra. We also show that the $s$-matrix interchanges tensor product with a much simpler product ("convolution product"), which can be used to compute the tensor product multiplicities. | |
| dc.description | LaTeX,33 pages, many figures | |
| dc.identifier | https://arxiv.org/abs/math/0401119 | |
| dc.identifier | http://arxiv.org/abs/math/0401119 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69827 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Category Theory | |
| dc.title | On $G$--equivariant modular categories | |
| dc.type | text |