Finite Weyl groupoids

By Michael Cuntz, István Heckenberger. 2010

55 citations recorded by the source corpus.

Using previous results concerning the rank two and rank three cases, all connected simply connected Cartan schemes for which the real roots form a finite irreducible root system of arbitrary rank are determined. As a consequence one obtains the list of all crystallographic arrangements, a large subclass of the class of simplicial hyperplane arrangements. Supposing that the rank is at least three, the classification yields Cartan schemes of type $A$ and $B$, an infinite family of series involving the types $C$ and $D$, and $74$ sporadic examples.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0eb52bd91774f37b41ce31c2238da96eea166b03

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In Algebra and Number Theory

1. I. Angiono
2. N. Andruskiewitsch
3. István Heckenberger
4. Hans Jürgen Schneider
5. A. Masuoka
6. Agustín García Iglesias
7. Leandro Vendramin
8. M. Graña

In Discrete Mathematics and Combinatorics

1. N. Andruskiewitsch
2. I. Angiono
3. István Heckenberger
4. Hans Jürgen Schneider
5. Agustín García Iglesias

In Mathematical Physics

1. I. Angiono
2. N. Andruskiewitsch

Citations in the corpus

• On finite-dimensional Hopf algebras (2014, background): “t B(M) ≃ ⊗l∈LB(Wl) as Zθ-graded objects in H HYD, where degx = βl for all x ∈ Wl, l ∈ L. Let ∆M ± = {±βl : l ∈ L}, ∆M = ∆M + ∪ ∆M − , ∆ = (∆ N) N∈X(M). Then R = (X,ρ,C,∆) is a finite GRS. Theorem 3.6. [23] The classification of all finite GRS is known. The proof is a combinatorial tour-de-force and req”
• On finite dimensional Nichols algebras of diagonal type (2017, background): “(b) Later, the classification of the finite generalized root systems was obtained in [36].”