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- W4311723218 abstract "In this paper we construct odd finitely summable spectral triples based on length functions of bounded doubling on noncommutative solenoids. Our spectral triples induce a Leibniz Lip-norm on the state spaces of the noncommutative solenoids, giving them the structure of Leibniz quantum compact metric spaces. By applying methods of R. Floricel and A. Ghorbanpour, we also show that our odd spectral triples on noncommutative solenoids can be considered as direct limits of spectral triples on rotation algebras. In the final section we prove a noncommutative Wiener's lemma and show that our odd spectral triples can be defined to have an associated smooth dense subalgebra which is stable under the holomorphic functional calculus, thus answering a question of B. Long and W. Wu. The construction of the smooth subalgebra also extends to the case of nilpotent discrete groups." @default.
- W4311723218 created "2022-12-28" @default.
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- W4311723218 date "2022-12-14" @default.
- W4311723218 modified "2023-10-14" @default.
- W4311723218 title "Spectral Triples for Noncommutative Solenoids and a Wiener's lemma" @default.
- W4311723218 doi "https://doi.org/10.48550/arxiv.2212.07470" @default.
- W4311723218 hasPublicationYear "2022" @default.
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