Spectral triples with multitwisted real structure
Abstract
We generalize the notion of spectral triple with reality structure to spectral triples with multitwisted real structure, 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 firstorder differential operator). This provides a unified description of the known examples, which include rescaled triples with the conformal factor from the commutant of the algebra and (on the algebraic level) triples on quantum disc and on quantum cone, that satisfy twisted first order condition of \cite{BCDS16,BDS19}, as well as asymmetric tori, nonscalar 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 DOI:
 10.48550/arXiv.1911.12873
 arXiv:
 arXiv:1911.12873
 Bibcode:
 2019arXiv191112873D
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematical Physics;
 58B34;
 58B32;
 46L87
 EPrint:
 12 pages