Transmutation and Bosonisation of Quasi-Hopf Algebras
| dc.creator | Klim, J | |
| dc.date | 2009-03-24 | |
| dc.date.accessioned | 2026-07-07T12:56:00Z | |
| dc.date.available | 2026-07-07T12:56:00Z | |
| dc.description | Let $H$ be a quasitriangular quasi-Hopf algebra, we construct a braided group $\underline{H}$ in the quasiassociative category of left $H$-modules. Conversely, given any braided group $B$ in this category, we construct a quasi-Hopf algebra $B\rtimes H$ in the category of vector spaces. We generalise the transmutation and bosonisation theory of [10] to the quasi case. As examples, we bosonise the octonion algebra to an asoociative one, obtain the twisted quantum double $D^ϕ(G)$ of a finite group as a bosonisation, and obtain its transmutation. Finally, we show that $\underline{H}\rtimes H$ is isomorphic to $H_\Rcal\blackbowtie H$ as quasi-Hopf algebras. | |
| dc.description | 35 pages latex, no figures | |
| dc.identifier | https://arxiv.org/abs/0903.3959 | |
| dc.identifier | http://arxiv.org/abs/0903.3959 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224442 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Mathematical Physics | |
| dc.subject | Rings and Algebras | |
| dc.title | Transmutation and Bosonisation of Quasi-Hopf Algebras | |
| dc.type | text |