2018/04/19 by Michel Dubois‐Violette, Michel Dubois-Violette, Xiao Han +1
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Character (mathematics) #Geometry #Invariant (physics) #Mathematical physics #Mathematics #Noncommutative algebraic geometry #Noncommutative geometry #Noncommutative quantum field theory #Physics #Projection (relational algebra) #Pure mathematics #Quantum mechanics #SPHERES #math-ph #math.MP #math.QA
paper · pdf · doi:10.1142/s0129055x18500204
arxiv created 2018/04/19 · openalex publication_date 2018/08/17 · arxiv updated 2018/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present examples of noncommutative four-spheres that are base spaces of SU(2)-principal bundles with noncommutative seven-spheres as total spaces. The noncommutative coordinate algebras of the four-spheres are generated by the entries of a projection which is invariant under the action of SU(2). We give conditions for the components of the Connes–Chern character of the projection to vanish but the second (the top) one. The latter is then a non-zero Hochschild cycle that plays the role of the volume form for the noncommutative four-spheres.