Computing finite Weyl groupoids

2025/05/30 by Iván Angiono, Angiono, Iván, Leandro Vendramin +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2505.24555

openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present algorithms to compute generalized root systems of Nichols algebras of diagonal type and of contragredient Lie superalgebras. As a consequence, we obtain an algorithm to compute the Lyndon words in the Kharchenko PBW basis associated to each positive root, along with their corresponding hyperwords. This data is essential for obtaining a minimal presentation of Nichols algebras of diagonal type with a finite root system.

Citations

• Finite GK-dimensional Nichols algebras of diagonal type and finite root systems
• On finite GK-dimensional Nichols algebras of diagonal type: rank 3 and Cartan type
• Liftings of Nichols algebras of diagonal type II. All liftings are\n cocycle deformations
• Finite Weyl groupoids
• A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
• Finite Weyl groupoids of rank three
• Drinfel'd doubles and Shapovalov determinants
• Weyl groupoids of rank two and continued fractions
• The Nichols algebra of a semisimple Yetter-Drinfeld module
• Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type
• A generalization of Coxeter groups, root systems, and Matsumoto's theorem
• Classification of arithmetic root systems

Related

• On Finite dimensional Nichols algebras of diagonal type
• Rank 2 Nichols algebras with finite arithmetic root system
• A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
• Finite Weyl groupoids of rank three
• Higher rank Nichols algebras of diagonal type with finite arithmetic root system in positive characteristic