Nichols algebras with many cubic relations

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.

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

References in corpus (1)

• Nichols algebras of group type with many quadratic relations

Cited by in corpus (7)

• The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
• On Fomin--Kirillov Algebras for Complex Reflection Groups
• Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension
• Multinomial expansion and Nichols algebras associated to non-degenerate involutive solutions of the Yang-Baxter equation
• Factorization of Graded Traces on Nichols Algebras
• Hurwitz Orbits with a Cellular Automaton
• On the Cycle Structure of Finite Racks and Quandles