Aldo J. Lazar

QUANTUM GROUPS AND DUALITY

We present an approach to the duality theory for quantum groups which is explicitly modelled on the construction of the group C*-algebra C* (G) from C0 (G), namely: in the dual of C0 (G), single out the ideal of all elements absolutely continuous with respect to Haar measure, renorm with a C*-norm determined by the representations of this ideal, and complete. We thus obtain a C*-algebra whose *-representations are in one-to-one correspondence with the representations of the quantum group. This C*-algebra is itself a (non-compact) quantum group, and we verify a duality theorem for it.

Crossed products of type I af algebras by abelian groups

Let (G, A, α) be a separableC*-dynamical system, withG abelian, and let Γ denote the dual group ofG. We characterize the Γ-invariant ideals of the crossed product algebraG×∩A, and use this characterization to prove that if in additionG is compact andA is type I AF, thenG×∩A is AF also. Finally, assumingG is discrete abelian and bothA andG×∩A are type I. we determine necessary and sufficient conditions, in terms ofA and the isotropy subgroups for the action ofG onÂ, forG×∩A to be AF.

The space of ideals in the minimal tensor product of C*-algebras

For

Pure state extensions of the trace on the Choi algebra

C^*

Compact group actions on C∗-algebras: An application of non-commutative duality

-algebras

SIMULTANEOUS LIFTING FROM IRREDUCIBLE REPRESENTATIONS OF

A_1, A_2

C^*

the map

-ALGEBRAS

(I_1,I_2)\to ker(q_{I_1}\otimes q_{I_2})

Applications of Non-Commutative Duality to Crossed Product C*-Algebras Determined by an Action or Coaction

from

Quotient spaces determined by algebras of continuous functions

Id^{\prime}(A_1)\times Id^{\prime}(A_2)