Pseudosymmetric braidings, twines and twisted algebras
| dc.creator | Panaite, Florin | |
| dc.creator | Staic, Mihai D. | |
| dc.creator | Van Oystaeyen, Freddy | |
| dc.date | 2008-01-14 | |
| dc.date.accessioned | 2026-07-07T08:54:19Z | |
| dc.date.available | 2026-07-07T08:54:19Z | |
| dc.description | A laycle is the categorical analogue of a lazy cocycle. Twines (as introduced by Bruguieres) and strong twines (as introduced by the authors) are laycles satisfying some extra conditions. If $c$ is a braiding, the double braiding $c^2$ is always a twine; we prove that it is a strong twine if and only if $c$ satisfies a sort of modified braid relation (we call such $c$ pseudosymmetric, as any symmetric braiding satisfies this relation). It is known that symmetric Yetter-Drinfeld categories are trivial; we prove that the Yetter-Drinfeld category $_H{\cal YD}^H$ over a Hopf algebra $H$ is pseudosymmetric if and only if $H$ is commutative and cocommutative. We introduce as well the Hopf algebraic counterpart of pseudosymmetric braidings under the name pseudotriangular structures and prove that all quasitriangular structures on the $2^{n+1}$-dimensional pointed Hopf algebras E(n) are pseudotriangular. We observe that a laycle on a monoidal category induces a so-called pseudotwistor on every algebra in the category, and we obtain some general results (and give some examples) concerning pseudotwistors, inspired by properties of laycles and twines. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/0801.2055 | |
| dc.identifier | http://arxiv.org/abs/0801.2055 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145886 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Category Theory | |
| dc.title | Pseudosymmetric braidings, twines and twisted algebras | |
| dc.type | text |