Crossed modules and quantum groups in braided categories
| dc.creator | Bespalov, Yu. N. | |
| dc.date | 1995-10-12 | |
| dc.date.accessioned | 2026-07-07T09:16:42Z | |
| dc.date.available | 2026-07-07T09:16:42Z | |
| dc.description | Let $A$ be a Hopf algebra in a braided category $\cal C$. Crossed modules over $A$ are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category $\DY{\cal C}^A_A$ of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group $(A,\overline A,{\cal R})$ the corresponding braided category of modules ${\cal C}_{\cO{A,\overline A}}$ is identified with a full subcategory in $\DY{\cal C}_A^A$. The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid--Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized. | |
| dc.description | 54 pages, latex, 28 figures prepared by latex This is a completely revised and complemented version of hep-th/9408102,hep-th/9408106 submitted to {\it Appl. Categorical Structures} | |
| dc.identifier | https://arxiv.org/abs/q-alg/9510013 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9510013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153448 | |
| dc.subject | Quantum Algebra | |
| dc.title | Crossed modules and quantum groups in braided categories | |
| dc.type | text |