Classification of Bicovariant Differential Calculi on the Quantum Groups $SL_q(n+1)$ and $Sp_q(2n)$
| dc.creator | Heckenberger, I. | |
| dc.creator | Schmuedgen, K. | |
| dc.date | 1997-07-25 | |
| dc.date | 1998-04-22 | |
| dc.date.accessioned | 2026-07-07T09:08:50Z | |
| dc.date.available | 2026-07-07T09:08:50Z | |
| dc.description | For transcendental values of $q$ all bicovariant first order differential calculi on the coordinate Hopf algebras of the quantum groups $SL_q(n+1)$ and $Sp_q(2n)$ are classified. It is shown that the irreducible bicovariant first order calculi are determined by an irreducible corepresentation of the quantum group and a complex number $ζ$ such that $ζ^{n+1}=1$ for $SL_q(n+1)$ and $ζ^2=1$ for $Sp_q(2n)$. Any bicovariant calculus is inner and its quantum Lie algebra is generated by a central element. The main technical ingredient is a result of the Hopf algebra $R(G_q)^0$ for arbitrary simple Lie algebras. | |
| dc.description | 21 pages, LaTeX2e, uses amstex.sty; extended version. To appear in J. reine angew. Math. (Crelle's Journal) | |
| dc.identifier | https://arxiv.org/abs/q-alg/9707032 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9707032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150862 | |
| dc.subject | Quantum Algebra | |
| dc.title | Classification of Bicovariant Differential Calculi on the Quantum Groups $SL_q(n+1)$ and $Sp_q(2n)$ | |
| dc.type | text |