Finite Weyl groupoids of rank three

Cuntz, M.; Heckenberger, I.

doi:10.1090/S0002-9947-2011-05368-7

Finite Weyl groupoids of rank three
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by M. Cuntz and I. Heckenberger

Trans. Amer. Math. Soc. 364 (2012), 1369-1393

DOI: https://doi.org/10.1090/S0002-9947-2011-05368-7

Published electronically: September 2, 2011

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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.

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