Vol. 3, No. 3, 2009
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Weyl groupoids of rank two and continued fractions

Michael Cuntz and István Heckenberger
Vol. 3 (2009), No. 3, 317–340
DOI: 10.2140/ant.2009.3.317
Abstract

We present a relationship between continued fractions and Weyl groupoids of Cartan schemes of rank two. This allows one 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.

Keywords
Cartan matrix, continued fraction, Nichols algebra, Weyl groupoid
Mathematical Subject Classification 2000
Primary: 20F55
Secondary: 11A55, 16W30
Milestones
Received: 1 July 2008
Revised: 19 January 2009
Accepted: 6 March 2009
Published: 1 May 2009
Authors
Michael Cuntz
Fachbereich Mathematik
Universität Kaiserslautern
Postfach 3049
D-67653 Kaiserslautern
Germany
http://www.mathematik.uni-kl.de/~cuntz/en/index.html
István Heckenberger
Mathematisches Institut
Ludwig-Maximilians-Universität München
Theresienstr. 39
D-80333 München
Germany
http://www.mi.uni-koeln.de/~iheckenb/istvane.html