Twisted spectral triples and covariant differential calculi

Ulrich Krähmer, and Elmar Wagner. "Twisted spectral triples and covariant differential calculi." Banach Center Publications 93.1 (2011): 177-188. <http://eudml.org/doc/281748>.

@article{UlrichKrähmer2011,
abstract = {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).},
author = {Ulrich Krähmer, Elmar Wagner},
journal = {Banach Center Publications},
keywords = {noncommutative geometry; compact quantum group; twisted spectral triple; covariant differential calculus},
language = {eng},
number = {1},
pages = {177-188},
title = {Twisted spectral triples and covariant differential calculi},
url = {http://eudml.org/doc/281748},
volume = {93},
year = {2011},
}

TY - JOUR
AU - Ulrich Krähmer
AU - Elmar Wagner
TI - Twisted spectral triples and covariant differential calculi
JO - Banach Center Publications
PY - 2011
VL - 93
IS - 1
SP - 177
EP - 188
AB - 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).
LA - eng
KW - noncommutative geometry; compact quantum group; twisted spectral triple; covariant differential calculus
UR - http://eudml.org/doc/281748
ER -