Irreducible representations of pointed Hopf algebras of type A₂

2025/07/29 by Iglesias, Agustín García, Rodriguez, Alfio Antonio
#16T05 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.21978

Abstract

We classify the irreducible representations of a family of finite-dimensional pointed liftings H_λ of the Nichols algebra associated with the diagram A₂ with parameter q=-1. We show that these algebras have infinite representation type and construct an indecomposable H_λ-module of dimension n for each n∈ℕ. Finally, we study a semisimple category \underlineRep H_λ arising as a quotient of Rep H_λ.

Citations

• On the representations of a family of pointed Hopf algebras
• On the finite-dimensional representations of the double of the Jordan plane
• Hopf cocycles associated to pointed and copointed deformations over S3
• On the double of the Jordan plane
• Simple Modules of the Quantum Double of the Nichols Algebra of Unidentified Diagonal Type \mathfrakufo(7)
• Liftings of Nichols algebras of diagonal type II. All liftings are\n cocycle deformations
• From Hopf algebras to tensor categories
• On Nichols algebras of diagonal type
• Classification of arithmetic root systems

Related

• On the irreducible representations of a class of pointed Hopf algebras
• On the lifting of Nichols algebras
• Representations of Finite Dimensional Pointed Hopf Algebras over \mathbbz_n
• Pointed Hopf algebras of odd dimension and Nichols algebras over solvable groups
• Pointed Hopf algebras revisited, with a view from tensor categories