Noncommutative Balls and Mirror Quantum Spheres

Abstract

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 analyzed, and their relations with previously known examples are presented. Our construction generalizes that of Hajac, Matthes and Szymanski for `dimension 2', and leads to a new class of quantum spheres (already on the C*-algebra level) in all `even-dimensions'.

20 pages

References in corpus (4)

• The ideal structure of the C*-algebras of infinite graphs
• Quantum even spheres Sigma_q^2n from Poisson double suspension
• Stable rank of graph algebras. Type I graph algebras and their limits
• Stability of C^*-algebra associated with the twisted CCR

Cited by in corpus (8)

• Free Actions on C*-algebra Suspensions and Joins by Finite Cyclic Groups
• Towards a noncommutative Brouwer fixed-point theorem
• Non-surjective pullbacks of graph C*-algebras from non-injective pushouts of graphs
• Fredholm modules over graph C*-algebras
• Rigidity on Quantum Symmetry for a Certain Class of Graph C*-algebras
• The weak heat kernel asymptotic expansion and the quantum double suspension
• Quantum even-dimensional balls
• $C^{\ast }$-algebras associated to $C^{\ast }$-correspondences and applications to mirror quantum spheres