2007/01/31 by Jeong Hee Hong, Wojciech Szymański, Wojciech Szymanski · 19 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Astronomy #Mathematical physics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Quantum #Quantum mechanics #SPHERES #Theoretical physics #math.OA #math.QA #msc:46L65 #msc:46L87
paper · pdf · doi:10.1112/jlms/jdn003
published in Journal of the London Mathematical Society 77(3), 607-626 (Wiley) · 20 pages
arxiv created 2007/08/04 · openalex publication_date 2008/03/03 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the ‘even-dimensional’ case they correspond to the twisted canonical commutation relations of Pusz and Woronowicz. Then quantum spheres are constructed as double manifolds of noncommutative balls. Both C*-algebras and polynomial algebras of the objects in question are defined and analysed, and their relations with previously known examples are presented. Our construction generalizes that of Hajac, Matthes, and Szymański for ‘dimension 2’, and leads to a new class of quantum spheres (already on the C*-algebra level) in all ‘even dimensions’.