Quantum Lens Spaces and Principal Actions on Graph C-Algebras

Quantum Lens Spaces and Graph Algebras

We construct the C∗-algebra C(Lq(p;m1, . . . ,mn)) of continuous functions on the quantum lens space as the fixed point algebra for a suitable action of Zp on the algebra C(S2n−1 q ), corresponding to the quantum odd dimensional sphere. We show that C(Lq(p;m1, . . . ,mn)) is isomorphic to the graph algebra C∗ ( L (p;m1,...,mn) 2n−1 ) . This allows us to determine the ideal structure and, at lea...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Fiber bundles and Lie algebras of top spaces

In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

0 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...

Ergodic Actions of Universal Quantum Groups on Operator Algebras

We construct ergodic actions of compact quantum groups on C∗-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups. In particular, we construct: (1). an ergodic action of the compact quantum Au(Q) on the type IIIλ Powers factor Rλ for an appropriate positive Q ∈ GL(2, R); (2). an ergodic action of the compact...