2001/03/09 by Laurent Freidel, Kirill Krasnov · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math.QA
paper · pdf · doi:10.1063/1.1456255
published as J.Math.Phys. 43 (2002) 1737-1754 · 21 pages, many figures
arxiv created 2001/03/09 · openalex publication_date 2002/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We analyze the expansion of the fuzzy sphere non-commutative product in powers of the non-commutativity parameter. To analyze this expansion we develop a graphical technique that uses spin networks. This technique is potentially interesting in its own right as introducing spin networks of Penrose into non-commutative geometry. Our analysis leads to a clarification of the link between the fuzzy sphere non-commutative product and the usual deformation quantization of the sphere in terms of the star-product.