Cyclic Structure behind Modular Gaussian Curvature
Abstract
We propose a systematic scheme for computing the variation of rearrangement operators arising in the recently developed spectral geometry on noncommutative tori and $\theta$deformed Riemannian manifolds. It can be summarized as a category whose objects consists of spectral functions of the rearrangement operators and morphisms are generated by transformations associated to basic operations of the variational calculus. The generators of the morphisms fulfil most of the relations in Connes's cyclic category, but also include all the partial derivatives. Comparison with Hopf cyclic theory has also been made.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.08730
 Bibcode:
 2022arXiv220108730L
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Operator Algebras
 EPrint:
 20 pages