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The garden of quantum spheres

Ludwik Dąbrowski (2003)

Banach Center Publications

A list of known quantum spheres of dimension one, two and three is presented.

The structure of corings with a grouplike element

Tomasz Brzeziński (2003)

Banach Center Publications

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

Ulrich Krähmer, Elmar Wagner (2011)

Banach Center Publications

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...

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