Twisted spectral triples and covariant differential calculi
Volume 93 / 2011
Banach Center Publications 93 (2011), 177-188
MSC: Primary 58B32; Secondary 81R60.
DOI: 10.4064/bc93-0-14
Abstract
Connes and Moscovici recently studied “twisted” spectral triples $(A,H,D)$ in which the commutators $[D,a]$ are replaced by $D \circ a - \sigma(a) \circ D$, where $ \sigma $ 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 $SU(2)$.
