Quantum symmetry groups of noncommutative spheres
نویسنده
چکیده
We show that the noncommutative spheres of Connes and Landi are quantum homogeneous spaces for certain compact quantum groups. We give a general construction of homogeneous spaces which support noncommutative spin geometries.
منابع مشابه
Differential Calculus on Quantum Spheres
We study covariant differential calculus on the quantum spheres S q . A classification result for covariant first order differential ∗ calculi is proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher orde...
متن کاملNoncommutative Balls and Mirror Quantum Spheres
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...
متن کاملOn the Absence of Continuous Symmetries for Noncommutative 3-Spheres
A large class of noncommutative spherical manifolds was obtained recently from cohomology considerations. A one-parameter family of twisted 3-spheres was discovered by Connes and Landi, and later generalized to a three-parameter family by Connes and Dubois-Violette. The spheres of Connes and Landi were shown to be homogeneous spaces for certain compact quantum groups. Here we investigate whethe...
متن کامل0 D ec 2 01 5 NONCOMMUTATIVE LINE BUNDLES ASSOCIATED TO TWISTED MULTIPULLBACK QUANTUM ODD SPHERES
We construct a noncommutative deformation of odd-dimensional spheres that preserves the natural partition of the (2N + 1)-dimensional sphere into (N + 1)many solid tori. This generalizes the case N = 1 referred to as the Heegaard quantum sphere. Our twisted odd-dimensional quantum sphere C∗-algebras are given as multipullback C∗-algebras. We prove that they are isomorphic to the universal C∗-al...
متن کاملNoncommutative Spheres and Instantons
We report on some recent work on deformation of spaces, notably deformation of spheres, describing two classes of examples. The first class of examples consists of noncommutative manifolds associated with the so called θ-deformations which were introduced in [17] out of a simple analysis in terms of cycles in the (b,B)-complex of cyclic homology. These examples have non-trivial global features ...
متن کامل