Weyl groupoids of rank two and continued fractions
arXiv:0807.0124
Abstract
A relationship between continued fractions and Weyl groupoids of Cartan schemes of rank two is found. This allows to decide easily if a given Cartan scheme of rank two admits a finite root system. We obtain obstructions and sharp bounds for the entries of the Cartan matrices. Key words: Cartan matrix, continued fraction, Nichols algebra, Weyl groupoid
23 pages