On Nichols algebras of low dimension

Details On Nichols algebras of low dimension On Nichols algebras of low dimension

2000-04-10

arxiv.org/abs/math/0004062v1

Mathematics

Quantum Algebra

23 pages, AMS-LaTeX

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On Nichols algebras of low dimension does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Nichols algebras of low dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Nichols algebras of low dimension will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-266392