On Nichols algebras of low dimension
| dc.creator | Grana, Matias | |
| dc.date | 2000-04-10 | |
| dc.date.accessioned | 2026-07-07T04:34:42Z | |
| dc.date.available | 2026-07-07T04:34:42Z | |
| dc.description | This is a contribution to the classification program of pointed Hopf algebras. We give a generalization of the quantum Serre relations and propose a generalization of the Frobenius-Lusztig kernels in order to compute Nichols algebras of diagonal group type. With this, we classify Nichols algebras B(V) with dimension < 32 or with dimension p^3, p a prime number, when V lies in a Yetter-Drinfeld category over a finite group. With the so called Lifting Procedure, this allows to classify pointed Hopf algebras of index < 32 or p^3. In recent articles by Etingof-Schedler-Soloviev and Lu-Yan-Zhu, the authors deal with set-theoretical solutions to the Braid Equation. We propose here an homology theory for conjugate solutions (in the language of Lu-Yan-Zhu) which parameterizes usual solutions lying over set-theoretical conjugate ones. These usual solutions are modules in Yetter-Drinfeld categories over group algebras, and then they provide (after computing Nichols algebras and liftings of their bosonizations) families of pointed Hopf algebras. | |
| dc.description | 23 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0004062 | |
| dc.identifier | http://arxiv.org/abs/math/0004062 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59002 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16W30; 17B37 | |
| dc.title | On Nichols algebras of low dimension | |
| dc.type | text |