Squared Hopf algebras and reconstruction theorems
| dc.creator | Lyubashenko, Volodymyr V. | |
| dc.date | 1996-05-22 | |
| dc.date.accessioned | 2026-07-07T09:16:59Z | |
| dc.date.available | 2026-07-07T09:16:59Z | |
| dc.description | Given an abelian k-linear rigid monoidal category V, where k is a perfect field, we define squared coalgebras as objects of cocompleted V tensor V (Deligne's tensor product of categories) equipped with the appropriate notion of comultiplication. Based on this, (squared) bialgebras and Hopf algebras are defined without use of braiding. If V is the category of k-vector spaces, squared (co)algebras coincide with conventional ones. If V is braided, a braided Hopf algebra can be obtained from a squared one. Reconstruction theorems give equivalence of squared co- (bi-, Hopf) algebras in V and corresponding fibre functors to V (which is not the case with other definitions). Finally, squared quasitriangular Hopf coalgebra is a solution to the problem of defining quantum groups in braided categories. | |
| dc.description | Latex2e, 31 pages, to appear in the Proceedings of Banach Center Minisemester on Quantum Groups, November 1995 | |
| dc.identifier | https://arxiv.org/abs/q-alg/9605035 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9605035 | |
| dc.identifier | Proc. Workshop ``Quantum Groups and Quantum Spaces'' (Warszawa), Banach Center Publ., no. 40, Inst. Math. Polish Acad. Sci. (1997) 111--137 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153548 | |
| dc.subject | Quantum Algebra | |
| dc.title | Squared Hopf algebras and reconstruction theorems | |
| dc.type | text |