The Fourier transform on quantum Euclidean space.
The Frobenius theorem on -dimensional quantum hyperplane.
The garden of quantum spheres
A list of known quantum spheres of dimension one, two and three is presented.
The noncommutative Ward metric.
The structure of corings with a grouplike element
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the Cuntz-Quillen theorem relating existence of connections in a module to projectivity of this module is proven.
Twisted spectral triples and covariant differential calculi
Connes and Moscovici recently studied "twisted" spectral triples (A,H,D) in which the commutators [D,a] are replaced by D∘a - σ(a)∘D, where σ is a second representation of A on H. The aim of this note is to point out that this yields representations of arbitrary covariant differential calculi over Hopf algebras in the sense of Woronowicz. For compact quantum groups, H can be completed to a Hilbert space and the calculus is given by bounded operators. At the end, we discuss an explicit example of...