# Weyl groupoids of rank two and continued fractions

@article{Cuntz2008WeylGO, title={Weyl groupoids of rank two and continued fractions}, author={Michael Cuntz and Istv{\'a}n Heckenberger}, journal={arXiv: Group Theory}, year={2008} }

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

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