Albert Jeu-Liang Sheu

Leaf-preserving quantizations of PoissonSU(2) are not coalgebra homomorphisms

Although it has been found that some deformation quantizations of the PoissonSU(2) preserve symplectic leaves and some preserve the group (i.e. coalgebra) operation, this paper shows that a quantization ofSU(2) cannot be both leaf-preserving and group-preserving.

Reinhardt domains, boundary geometry, and Toeplitz C∗-algebras

Abstract In this paper, we have found explicitly how the boundary geometry of a Reinhardt domain in C 2 determines the structure of its Toeplitz C ∗ -algebra. More precisely, our main result is an explicit simple algorithm to describe the structure of the Toeplitz C ∗ -algebra of a Reinhardt domain D in C 2 (satisfying some mild boundary condition) in terms of rotation C ∗ -algebras, based on the degree of contact of the boundary curve of C , the logarithmic domain of D at each point of intersection with the linear faces of the convex hull of C , and the slopes of these faces. A consequence of this result is that the Toeplitz C ∗ -algebras T ( D ) and T ( D ) of D and its pseudoconvex hull D are rarely isomorphic, but are always of the same type (i.e., either both are of type I or both are not of type I). In other words, the isomorphism class of T ( D ) is usually changed under taking pseudoconvex hull but the type of T ( D ) is not affected.

The structure of quantum spheres

We show that the C*-algebra C ( S2n+1 q ) of a quantum sphere S2n+1 q , q > 1, consists of continuous fields {ft}t∈T of operators ft in a C*algebra A, which contains the algebra K of compact operators with A/K ∼= C ( S2n−1 q ) , such that ρ∗ (ft) is a constant function of t ∈ T, where ρ∗ : A → A/K is the quotient map and T is the unit circle.

Projective Modules Over Quantum Projective Line

Taking a groupoid C*-algebra approach to the study of the quantum complex projective spaces

Quasi Multiplication and K-groups

\mathbb{P}^{n}\left( \mathcal{T}\right)

Quantization of Poisson SU(2)

constructed from the multipullback quantum spheres introduced by Hajac and collaborators, we analyze the structure of the C*-algebra

Quantization of the PoissonSU(2) and its Poisson homogeneous space — The 2-sphere

C\left( \mathbb{P}^{1}\left( \mathcal{T}\right) \right)

Groupoid Approach to Quantum Projective Spaces

realized as a concrete groupoid C*-algebra, and find its

QUANTUM SPHERES AS GROUPOID C* -ALGEBRAS

K

Bott periodicity and calculus of Euler classes on spheres

-groups. Furthermore after a complete classification of the unitary equivalence classes of projections or equivalently the isomorphism classes of finitely generated projective modules over the C*-algebra