Weyl groupoids with at most three objects

Details Weyl groupoids with at most three objects Weyl groupoids with at most three objects

2008-05-13

arxiv.org/abs/0805.1810v1

Mathematics

Group Theory

31 pages

Scientific paper

We adapt the generalization of root systems of the second author and H. Yamane to the terminology of category theory. We introduce Cartan schemes, associated root systems and Weyl groupoids. After some preliminary general results, we completely classify all finite Weyl groupoids with at most three objects. The classification yields that there exist infinitely many standard, but only 9 exceptional cases. Key words: Nichols algebra, reflection, root system, Weyl groupoid

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