Abstract
AbstractWe demonstrate how to construct spectral triples for twisted group $$C^*$$
C
∗
-algebras of lattices in phase space of a second-countable locally compact abelian group using a class of weights appearing in time–frequency analysis. This yields a way of constructing quantum $$C^k$$
C
k
-structures on Heisenberg modules, and we show how to obtain such structures using Gabor analysis and certain weighted analogues of Feichtinger’s algebra. We treat the standard spectral triple for noncommutative 2-tori as a special case, and as another example we define a spectral triple on noncommutative solenoids and a quantum $$C^k$$
C
k
-structure on the associated Heisenberg modules.
Funder
NTNU Norwegian University of Science and Technology
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference40 articles.
1. Arambašić, L., Bakić, D.: Frames and outer frames for Hilbert $$C^{\ast }$$-modules. Linear Multilinear Algebra 65(2), 381–431 (2017)
2. Austad, A.: Spectral invariance of $$\ast$$-representations of twisted convolution algebras with applications in Gabor analysis. arXiv:2002.02235v2 (2020)
3. Austad, A., Enstad, U.: Heisenberg modules as function spaces. J. Fourier Anal. Appl. 26(2), 24 (2020). https://doi.org/10.1007/s00041-020-09729-7
4. Austad, A., Jakobsen, M.S., Luef, F.: Gabor duality theory for Morita equivalent $$C^{\ast }$$-algebras. Int. J. Math. 31(10), 2050073 (2020)
5. Bédos, E., Omland, T.: On reduced twisted group $$C^{\ast }$$-algebras that are simple and/or have a unique trace. J. Noncommut. Geom. 12(3), 947–996 (2018)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Real spectral triples on crossed products;Reviews in Mathematical Physics;2022-08-06