Classification of differentials and Cartan calculus on bicrossproducts
| dc.creator | Ngakeu, F. | |
| dc.creator | Majid, S. | |
| dc.creator | Ezin, J-P. | |
| dc.date | 2002-05-17 | |
| dc.date | 2003-10-09 | |
| dc.date.accessioned | 2026-07-07T04:48:34Z | |
| dc.date.available | 2026-07-07T04:48:34Z | |
| dc.description | We provide the Cartan calculus for bicovariant differential forms on bicrossproduct quantum groups $k(M)\lrbicross kG$ associated to finite group factorizations $X=GM$ and a field $k$. The irreducible calculi are associated to certain conjugacy classes in $X$ and representations of isotropy groups. We find the full exterior algebras and show that they are inner by a bi-invariant 1-form $θ$ which is a generator in the noncommutative de Rham cohomology $H^1$. The special cases where one subgroup is normal are analysed. As an application, we study the noncommutative cohomology on the quantum codouble $D^*(S_3)\isom k(S_3)\lrbicross k\Z_6$ and the quantum double $D(S_3)=k(S_3)\lcross kS_3$, finding respectively a natural calculus and a unique calculus with $H^0=k.1$. | |
| dc.description | Minor revision: deleted six pages (mainly some examples) at request of referee. Now 30 pages latex, no figs | |
| dc.identifier | https://arxiv.org/abs/math/0205194 | |
| dc.identifier | http://arxiv.org/abs/math/0205194 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64095 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Differential Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 58B32, 58B34 | |
| dc.title | Classification of differentials and Cartan calculus on bicrossproducts | |
| dc.type | text |