2006/03/11 by David E. Radford, Hans-Jürgen Schneider, Hans‐Jürgen Schneider +2
Mathematics · Physics and Astronomy · #16W30 #17B10 #17B37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:16W30 #msc:17B10 #msc:17B37
paper · pdf · doi:10.48550/arxiv.math/0603270
amstex, 33 pages
arxiv created 2006/03/11 · openalex publication_date 2006/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let U and A be algebras over a field k. We study algebra structures H on the underlying tensor product U⊗A of vector spaces which satisfy (u⊗a)(u'⊗a') = uu'⊗aa' if a = 1 or u' = 1. For a pair of characters ρ∈ \Alg(U, k) and χ∈ \Alg(A, k) we define a left H-module L(ρ, χ). Under reasonable hypotheses the correspondence (ρ, χ) ↦ L(ρ, χ) determines a bijection between character pairs and the isomorphism classes of objects in a certain category H\underline\mathcal M of left H-modules. In many cases the finite-dimensional objects of H\underline\mathcal M are the finite-dimensional irreducible left H-modules. In math.QA/0603269 we apply the results of this paper and show that the finite-dimensional irreducible representations of a wide class of pointed Hopf algebras are parameterized by pairs of characters.