Finite Weyl groupoids of rank three
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- by M. Cuntz and I. Heckenberger PDF
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Abstract:
We continue our study of Cartan schemes and their Weyl group- oids and obtain a complete list of all connected simply connected Cartan schemes of rank three for which the real roots form a finite irreducible root system. We achieve this result by providing an algorithm which determines all the root systems and eventually terminates: Up to equivalence there are exactly 55 such Cartan schemes, and the number of corresponding real roots varies between $6$ and $37$. We identify those Weyl groupoids which appear in the classification of Nichols algebras of diagonal type.References
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Additional Information
- M. Cuntz
- Affiliation: Fachbereich Mathematik, Universität Kaiserslautern, Postfach 3049, D-67653 Kaiserslautern, Germany
- Email: cuntz@mathematik.uni-kl.de
- I. Heckenberger
- Affiliation: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans- Meerwein-Straße, D-35032 Marburg, Germany
- MR Author ID: 622688
- Email: heckenberger@mathematik.uni-marburg.de
- Received by editor(s): December 4, 2009
- Received by editor(s) in revised form: March 22, 2010, March 25, 2010, and April 7, 2010
- Published electronically: September 2, 2011
- Additional Notes: The second author was supported by the German Research Foundation (DFG) via a Heisenberg fellowship
- © Copyright 2011 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 364 (2012), 1369-1393
- MSC (2010): Primary 20F55, 16T30, 52C30
- DOI: https://doi.org/10.1090/S0002-9947-2011-05368-7
- MathSciNet review: 2869179