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Twisted spectral triples and covariant differential calculi

Volume 93 / 2011

Ulrich Krähmer, Elmar Wagner 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 $SU(2)$.

Authors

  • Ulrich KrähmerSchool of Mathematics and Statistics
    University of Glasgow
    15 University Gardens
    Glasgow G12 8QW, Scotland
    e-mail
  • Elmar WagnerInstituto de Física y Matemáticas
    Universidad Michoacana de San Nicolás de Hidalgo
    Edificio C-3
    Cd. Universitaria
    58040 Morelia, Michoacán, México
    e-mail

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