Classification of arithmetic root systems of rank 3

2005/09/07 by Heckenberger, I.
#16W35 #17B37 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.math/0509145

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

Related

• Classification of arithmetic root systems
• Rank 2 Nichols algebras with finite arithmetic root system
• Rank three Nichols algebras of diagonal type over fields of positive characteristic
• Rank 4 finite-dimensional Nichols algebras of diagonal type in positive characteristic
• Higher rank Nichols algebras of diagonal type with finite arithmetic root system in positive characteristic