Pith. sign in

REVIEW 1 cited by

Spin geometry of the rational noncommutative torus

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1804.06803 v2 pith:2SVKDDZM submitted 2018-04-18 math.QA math-phmath.MPmath.OA

classification math.QAmath-phmath.MPmath.OA
keywords spectralnoncommutativetorustriplealgebracertainisomorphismsparameter
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

The twined almost commutative structure of the standard spectral triple on the noncommutative torus with rational parameter is exhibited, by showing isomorphisms with a spectral triple on the algebra of sections of certain bundle of algebras, and a spectral triple on a certain invariant subalgebra of the product algebra. These isomorphisms intertwine also the grading and real structure. This holds for all four inequivalent spin structures, which are explicitly constructed in terms of double coverings of the noncommutative torus (with arbitrary real parameter). These results are extended also to a class of curved (non flat) spectral triples, obtained as a perturbation of the standard one by eight central elements.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Finite spectral triples for the fuzzy torus

    math.QA 2019-08 accept novelty 6.0 of 10

    A finite spectral triple for the fuzzy torus is constructed whose Dirac spectrum is the q-integer analogue of the commutative flat torus spectrum, for all four spin structures.

Pith tools