Realization ofU q (so(N)) within the differential algebra onR q N

1994/03/04 by Gaetano Fiore · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Current algebra #Differential (mechanical device) #Differential operator #Euclidean geometry #Geometry #Hopf algebra #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum algebra #Realization (probability) #hep-th #math.QA

paper · pdf · doi:10.1007/bf02099309

published as Commun.Math.Phys.169:475-500,1995 · 26 pages, 1 figure

arxiv created 1994/03/04 · openalex publication_date 1995/05/01 · arxiv updated 2014/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We realize the Hopf algebra U_q^-1(so(N)) as an algebra of differential operators on the quantum Euclidean space \bf R_q^N. The generators are suitable q-deformed analogs of the angular momentum components on ordinary \bf R^N. The algebra Fun(\bf R_q^N) of functions on \bf R_q^N splits into a direct sum of irreducible vector representations of U_q^-1(so(N)); the latter are explicitly constructed as highest weight representations.

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