Simple tensor products

2009/07/31 by David Hernandez · 34 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine transformation #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Product (mathematics) #Quantum #Simple (philosophy) #Tensor (intrinsic definition) #Tensor product #Tensor product of Hilbert spaces #Tensor product of modules #math.QA #math.RT

paper · pdf · doi:10.1007/s00222-010-0256-9

published in Inventiones mathematicae 181(3), 649-675 (Springer Science+Business Media) · 21 pages ; accepted for publication in Inventiones Mathematicae

arxiv created 2010/05/07 · openalex publication_date 2010/05/21 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

Let F be the category of finite dimensional representations of an arbitrary quantum affine algebra. We prove that a tensor product S₁⊗ ... ⊗ S_N of simple objects of F is simple if and only if for any i < j, S_i⊗ S_j is simple.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups

Cited by

• Cyclicity and R-matrices
• Monoidal categorification and quantum affine algebras