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 Heckenberger's 3-dimensional covariant differential calculi on quantum SU(2).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-14,
author = {Ulrich Kr\"ahmer and Elmar Wagner},
title = {Twisted spectral triples and covariant differential calculi},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {177-188},
zbl = {1253.58003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-14}
}
Ulrich Krähmer; Elmar Wagner. Twisted spectral triples and covariant differential calculi. Banach Center Publications, Tome 95 (2011) pp. 177-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-14/