Special biserial coalgebras and representations of quantum SL(2)

2006/09/13 by William Chin, Chin, William
Mathematics · Physics and Astronomy · #16G70 #16W30 #17B37 #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.QA #math.RA #math.RT #msc:16G70 #msc:16W30 #msc:17B37 #msc:20G42

paper · pdf · doi:10.48550/arxiv.math/0609370

previous section 2.2 removed, errors corrected

openalex publication_date 2006/09/13 · arxiv created 2011/03/23 · arxiv updated 2011/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the theory of special biserial and string coalgebras and other concepts from the representation theory of quivers. These tools are then used to describe the finite dimensional comodules and Auslander-Reiten quiver for the coordinate Hopf algebra of quantum SL(2) at a root of unity. We also describe the stable Green ring and compute quantum dimensions.

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