Factorization of simple modules for certain pointed Hopf algebras

2007/02/21 by Mariana Pereira, Pereira, Mariana
Mathematics · Physics and Astronomy · #16W30 #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16W30 #msc:20G42

paper · pdf · doi:10.48550/arxiv.math/0702614

24 pages

openalex publication_date 2007/02/21 · arxiv created 2007/04/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the representations of two types of pointed Hopf algebras: restricted two-parameter quantum groups, and the Drinfel'd doubles of rank one pointed Hopf algebras of nilpotent type. We study, in particular, under what conditions a simple module can be factored as the tensor product of a one dimensional module with a module that is naturally a module for the quotient by central group-like elements.

Citations

• Normal basis and transitivity of crossed products for Hopf algebras

Related

• Module categories over pointed Hopf algebras
• Simple modules over finite quantum groups and their Drinfel'd doubles
• Representations of pointed Hopf algebras and their Drinfel'd quantum doubles
• Quantum doubles of certain rank two pointed Hopf algebras
• Modularization of small quantum groups