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Nichols algebras with many cubic relations


Authors: I. Heckenberger, A. Lochmann and L. Vendramin
Journal: Trans. Amer. Math. Soc. 367 (2015), 6315-6356
MSC (2010): Primary 16T05; Secondary 20F99, 16P90
Published electronically: January 30, 2015
MathSciNet review: 3356939
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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 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.


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Additional Information

I. Heckenberger
Affiliation: FB Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein- Straße, 35032 Marburg, Germany
Email: heckenberger@mathematik.uni-marburg.de

A. Lochmann
Affiliation: FB Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein- Straße, 35032 Marburg, Germany
Email: lochmann@mathematik.uni-marburg.de

L. Vendramin
Affiliation: FB Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein- Straße, 35032 Marburg, Germany
Email: lvendramin@dm.uba.ar

DOI: https://doi.org/10.1090/S0002-9947-2015-06231-X
Received by editor(s): February 3, 2013
Received by editor(s) in revised form: June 25, 2013
Published electronically: January 30, 2015
Additional Notes: The first author was supported by the German Research Foundation via a Heisenberg professorship
The third author was supported by CONICET and the Alexander von Humboldt Foundation
Article copyright: © Copyright 2015 American Mathematical Society