We study some aspects of the theory of non-commutative differential calculi over complex algebras, especially over the Hopf algebras associated to compact quantum groups in the sense of S.L.â€¦ (More)

We consider the Markov operator PÏ† on a discrete quantum group given by convolution with a q-tracial state Ï†. In the study of harmonic elements x, PÏ†(x) = x, we define the Martin boundary AÏ†. It is aâ€¦ (More)

For the Dirac operatorD on the standard quantum sphere we obtain an asymptotic expansion of the SUq(2)-equivariant entire cyclic cocycle corresponding to Îµ 1 2D when evaluated on the element k âˆˆâ€¦ (More)

For the q-deformation Gq, 0 < q < 1, of any simply connected simple compact Lie group G we construct an equivariant spectral triple which is an isospectral deformation of that defined by the Diracâ€¦ (More)

We define concepts of amenability and coamenability for algebraic quantum groups in the sense of Van Daele (1998). We show that coamenability of an algebraic quantum group always implies amenabilityâ€¦ (More)

For an algebra B with an action of a Hopf algebra H we establish the pairing between equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantumâ€¦ (More)

We give a pedagogical survey of those aspects of the abstract representation theory of quantum groups which are related to the Tannaka-Krein reconstruction problem. We show that every concreteâ€¦ (More)

For an algebra B coming with an action of a Hopf algebra H and a twist automorphism, we introduce equivariant twisted cyclic cohomology. In the case when the twist is implemented by a modular elementâ€¦ (More)