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Spectral triples on irreversible C∗-dynamical systems.
- Source :
-
International Journal of Mathematics . Jan2022, Vol. 33 Issue 1, p1-35. 35p. - Publication Year :
- 2022
-
Abstract
- Given a spectral triple on a C ∗ -algebra together with a unital injective endomorphism α , the problem of defining a suitable crossed product C ∗ -algebra endowed with a spectral triple is addressed. The proposed construction is mainly based on the works of Cuntz and [A. Hawkins, A. Skalski, S. White and J. Zacharias, On spectral triples on crossed products arising from equicontinuous actions, Math. Scand. 113(2) (2013) 262–291], and on our previous papers [V. Aiello, D. Guido and T. Isola, Spectral triples for noncommutative solenoidal spaces from self-coverings, J. Math. Anal. Appl. 448(2) (2017) 1378–1412; V. Aiello, D. Guido and T. Isola, A spectral triple for a solenoid based on the Sierpinski gasket, SIGMA Symmetry Integrability Geom. Methods Appl. 17(20) (2021) 21]. The embedding of α () in can be considered as the dual form of a covering projection between noncommutative spaces. A main assumption is the expansiveness of the endomorphism, which takes the form of the local isometricity of the covering projection, and is expressed via the compatibility of the Lip-norms on and α (). [ABSTRACT FROM AUTHOR]
- Subjects :
- *ENDOMORPHISMS
*MATHEMATICS
*STEINER systems
Subjects
Details
- Language :
- English
- ISSN :
- 0129167X
- Volume :
- 33
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- International Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 155234704
- Full Text :
- https://doi.org/10.1142/S0129167X22500057