Double-Bosonisation and the Construction of {$U_q(g)$}
| dc.creator | Majid, S. | |
| dc.date | 1995-11-02 | |
| dc.date.accessioned | 2026-07-07T09:16:43Z | |
| dc.date.available | 2026-07-07T09:16:43Z | |
| dc.description | We introduce a quasitriangular Hopf algebra or `quantum group' $U(B)$, the {\em double-bosonisation}, associated to every braided group $B$ in the category of $H$-modules over a quasitriangular Hopf algebra $H$, such that $B$ appears as the `positive root space', $H$ as the `Cartan subalgebra' and the dual braided group $B^*$ as the `negative root space' of $U(B)$. The choice $B=f$ recovers Lusztig's construction of $U_q(g)$, where $f$ is Lusztig's algebra associated to a Cartan datum; other choices give more novel quantum groups. As an application, our construction provides a canonical way of building up quantum groups from smaller ones by repeatedly extending their positive and negative root spaces by linear braided groups; we explicitly construct $U_q(sl_3)$ from $U_q(sl_2)$ by this method, extending it by the quantum-braided plane $A_q^2$. We provide a fundamental representation of $U(B)$ in $B$. A projection from the quantum double, a theory of double biproducts and a Tannaka-Krein reconstruction point of view are also provided. | |
| dc.description | LATEX 57 pages and epsf figures | |
| dc.identifier | https://arxiv.org/abs/q-alg/9511001 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9511001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153454 | |
| dc.subject | Quantum Algebra | |
| dc.title | Double-Bosonisation and the Construction of {$U_q(g)$} | |
| dc.type | text |