Finite Weyl groupoids of rank three

DOI10.1090/S0002-9947-2011-05368-7zbMath1246.20037arXiv0912.0212OpenAlexW2963772909MaRDI QIDQ2880684

Michael Cuntz, István Heckenberger

Publication date: 13 April 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0212

zbMATH Keywords

algorithmsNichols algebrasWeyl groupoidsCartan schemes of rank threefinite irreducible root systems

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Planar arrangements of lines and pseudolines (aspects of discrete geometry) (52C30) Connections of Hopf algebras with combinatorics (16T30) Root systems (17B22)

Related Items (22)

Distinguished pre-Nichols algebras ⋮ Algebras of non-local screenings and diagonal Nichols algebras ⋮ Congruence normality of simplicial hyperplane arrangements via oriented matroids ⋮ A greedy algorithm to compute arrangements of lines in the projective plane ⋮ Bruhat order and nil-Hecke algebras for Weyl groupoids ⋮ Rank 4 finite-dimensional Nichols algebras of diagonal type in positive characteristic ⋮ Finite GK-dimensional pre-Nichols algebras of super and standard type ⋮ A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems. ⋮ Pointed Hopf algebras over nonabelian groups with nonsimple standard braidings ⋮ Strongly symmetric smooth toric varieties ⋮ Coxeter and crystallographic arrangements are inductively free ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type. I: Non-semisimple classes in \(\mathbf{PSL}_n(q)\). ⋮ Finite Cartan graphs attached to Nichols algebras of diagonal type ⋮ A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups ⋮ Rank three Nichols algebras of diagonal type over arbitrary fields ⋮ A bound for crystallographic arrangements ⋮ The R-matrix of quantum doubles of Nichols algebras of diagonal type ⋮ Simplicial arrangements with up to 27 lines ⋮ Arrangements of ideal type are inductively free ⋮ Cohomology rings of finite-dimensional pointed Hopf algebras over abelian groups ⋮ On the Tits cone of a Weyl groupoid ⋮ Virasoro Central Charges for Nichols Algebras

Cites Work

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• Weyl groupoids with at most three objects.
• Weyl groupoids of rank two and continued fractions.
• Reflection groupoids of rank two and cluster algebras of type \(A\)
• Rank 2 Nichols algebras with finite arithmetic root system
• A generalization of Coxeter groups, root systems, and Matsumoto's theorem.
• The Weyl groupoid of a Nichols algebra of diagonal type
• A catalogue of simplicial arrangements in the real projective plane
• Lie superalgebras

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