• Corpus ID: 208512949

Multitwisted real spectral triples

@article{Dabrowski2019MultitwistedRS,
  title={Multitwisted real spectral triples},
  author={Ludwik Da̧browski and Andrzej Sitarz},
  journal={arXiv: Quantum Algebra},
  year={2019}
}

• L. Da̧browski, A. Sitarz
• Published 28 November 2019
• Mathematics
• arXiv: Quantum Algebra

We generalize the notion of spectral triple with reality structure to multitwisted real spectral triples, the class of which is closed under the tensor product composition. In particular, we introduce a multitwisted order one condition (characterizing the Dirac operators as an analogue of first-order differential operator). This provides a unified description of the known examples, which include conformally rescaled triples and (on the algebraic level) triples on quantum disc and on quantum cone, that satisfy twisted first order condition, as well as asymmetric tori, non-scalar conformal rescaling and noncommutative circle bundles. In order to deal with them we allow twists that do not implement automorphisms of the algebra of spectral triple, in which case we need to generalize also the so called zero order condition that the adjoint action of the real structure takes the algebra to its commutant.