Module categories over pointed Hopf algebras

2008/11/25 by Martín Mombelli, Martin Mombelli, Mombelli, Martin · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Hopf algebra #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum group #Quantum mechanics #Tensor (intrinsic definition) #Tensor product #math.QA #math.RA #msc:16W30 #msc:18D10 #msc:19D23

paper · pdf · doi:10.48550/arxiv.0811.4090

published in arXiv (Cornell University) (Cornell University) · 31 pages, typos and other errors corrected. Some improvements on Lemma 5.5 have been done. Section 8.2 was corrected

openalex publication_date 2008/11/25 · arxiv created 2009/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop some techniques to the study of exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups u_q(\mathfraksl₂).

Cited by

• Freeness and divisibility for right H-simple left H-comodule algebras over a pointed Hopf algebra H
• H-Equivariant Morita equivalences of Loewy-graded comodule algebras

Related

• Module categories over finite pointed tensor categories
• Factorization of simple modules for certain pointed Hopf algebras
• Exact module categories over Rep(u_q(\mathfraksl₂))
• Pointed Hopf algebras revisited, with a view from tensor categories
• On the Classification of Finite Quasi-Quantum Groups over Abelian Groups