Nichols algebras with many cubic relations
Quantum Algebra
2015-10-29 v3 Combinatorics
Abstract
Nichols algebras of group type with many cubic relations are classified under a technical assumption on the structure of Hurwitz orbits of the third power of the underlying indecomposable rack. All such Nichols algebras are finite-dimensional and their Hilbert series have a factorization into quantum integers. Also, all known finite-dimensional elementary Nichols algebras of group type turn out to have many cubic relations. The technical assumption of our theorem can be removed if a conjecture in the theory of cellular automata can be proven.
Cite
@article{arxiv.1212.4330,
title = {Nichols algebras with many cubic relations},
author = {I. Heckenberger and A. Lochmann and L. Vendramin},
journal= {arXiv preprint arXiv:1212.4330},
year = {2015}
}
Comments
46 pages, 20 figures. We improved significantly the text by adding more definitions and more explanations. Accepted for publication in Transactions of the American Mathematical Society