English

Classification of arithmetic root systems of rank 3

Quantum Algebra 2016-09-07 v1

Abstract

The paper purposes to contribute to the classification of pointed Hopf algebras by the method of Andruskiewitsch and Schneider. The structure of arithmetic root systems is enlightened such that their relation to ordinary root systems associated to semi-simple Lie algebras becomes more astounding. As an application all arithmetic root systems of rank 3 are determined. The result gives in particular all finite dimensional rank 3 Nichols algebras of diagonal type over a field of characteristic zero. Key Words: Weyl groupoid, Hopf algebra, Nichols algebra

Keywords

Cite

@article{arxiv.math/0509145,
  title  = {Classification of arithmetic root systems of rank 3},
  author = {I. Heckenberger},
  journal= {arXiv preprint arXiv:math/0509145},
  year   = {2016}
}

Comments

30 pages, 2 tables, several figures

R2 v1 2026-07-22T17:24:14.736Z