2004/05/31 by Gaetano Fiore
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Antisymmetric relation #Antisymmetric tensor #Bimodule #Black Holes and Theoretical Physics #Covariant transformation #Differential form #Differential operator #Gauge theory #Group (periodic table) #Mathematical physics #Mathematics #Noncommutative geometry #Physics #Pure mathematics #Quantum mechanics #hep-th #math-ph #math.MP #math.QA #msc:17B37 #msc:81R50
paper · pdf · doi:10.1088/0305-4470/37/39/009
published as J. Phys. A: Math. Gen. 37 (2004), 9175-9193 · latex file, 24 pages. Some citations added and misprints corrected. Final version to appear in J. Phys. A Math. and Gen
arxiv created 2004/07/27 · openalex publication_date 2004/09/16 · arxiv updated 2012/09/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
GL q ( N )- and SO q ( N )-covariant deformations of the completely symmetric/antisymmetric projectors with an arbitrary number of indices are explicitly constructed as polynomials in the braid matrices. The precise relation between the completely antisymmetric projectors and the completely antisymmetric tensor is determined. Adopting the GL q ( N )- and SO q ( N )-covariant differential calculi on the corresponding quantum group covariant noncommutative spaces , we introduce a generalized notion of vielbein basis (or 'frame'), based on differential-operator-valued 1-forms. We then give a thorough definition of a SO q ( N )-covariant -bilinear Hodge map acting on the bimodule of differential forms on , introduce the exterior coderivative and show that the Laplacian acts on differential forms exactly as in the undeformed case, namely it acts on each component as it does on functions.