1993/08/30 by Shahn Majid
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th #math.QA
paper · pdf · doi:10.1063/1.530527
published as J.Math.Phys. 35 (1994) 2617-2632 · 24 pages
arxiv created 1993/08/30 · openalex publication_date 1994/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An addition law is introduced for the usual quantum matrices A(R) by means of a coaddition Δt=t⊗1+1⊗t. It supplements the usual comultiplication Δt=t⊗t and together they obey a codistributivity condition. The coaddition does not form a usual Hopf algebra but a braided one. The same remarks apply for rectangular m×n quantum matrices. As an application, left-invariant vector fields are constructed on A(R) and other quantum spaces. They close in the form of a braided Lie algebra. As another application, the wave functions in the lattice approximation of Kac–Moody algebras and other lattice fields can be added and functionally differentiated.