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Spheres, Euler classes and the K-theory of C*-algebras of subproduct systems
Multi angle
Authors : Arici, Francesca (Author of the conference)
CIRM (Publisher )
19K35 - Kasparov theory ($KK$-theory)
46L80 - K-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
46L85 - Noncommutative topology
46L08 - C*-modules
30H20 - Bergman spaces, Fock spaces
CIRM (Publisher )
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Abstract :
In this talk, we shall consider equivariant subproduct system of Hilbert spaces and their Toeplitz and Cuntz–Pimsner algebras. We will provide results about their topological invariants through K(K)-theory. More specifically, we will show that the Toeplitz algebra of the subproduct system of an SU(2)-representation is equivariantly KKequivalent to the algebra of complex numbers so that the (K)K- theory groups of the Cuntz–Pimsner algebra can be effectively computed using a Gysin exact sequence involving an analogue of the Euler class of a sphere bundle. Finally, we will discuss why and how C*-algebras in this class satisfy KK-theoretic Poincaré duality.
Keywords : Subproduct system; C*-correspondences; C*-algebras; KK-theory; operator K-theory
MSC Codes : Keywords : Subproduct system; C*-correspondences; C*-algebras; KK-theory; operator K-theory
19K35 - Kasparov theory ($KK$-theory)
46L80 - K-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
46L85 - Noncommutative topology
46L08 - C*-modules
30H20 - Bergman spaces, Fock spaces
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 13/05/2024 Conference Date : 23/04/2024 Subseries : Research talks arXiv category : Operator Algebras Mathematical Area(s) : Algebra ; Analysis and its Applications ; Geometry Format : MP4 (.mp4) - HD Video Time : 00:48:34 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-04-23_Arici.mp4 
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Information on the Event
Event Title : Group operator algebras and Non commutative geometry / Algèbres d'opérateurs de groupes et Geometrie non commutativeEvent Organizers : Androulidakis, Iakovos ; Debord, Claire ; Germain, Emmanuel ; Houdayer, Cyril Dates : 22/04/2024 - 26/04/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/2987.html
Citation Data
DOI : 10.24350/CIRM.V.20165403Cite this video as: Arici, Francesca (2024). Spheres, Euler classes and the K-theory of C*-algebras of subproduct systems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20165403 URI : http://dx.doi.org/10.24350/CIRM.V.20165403 |
See Also
- [Multi angle] Amenability and hyperfiniteness for group actions on trees / Author of the conference Spaas, Pieter.
- [Multi angle] On maximally hypoelliptic differential operators / Author of the conference Mohsen, Omar.
- [Multi angle] A gentle introduction to type III factors and Connes' Bicentralizer Problem / Author of the conference Marrakchi, Amine.
- [Multi angle] C*-algebras associated with boundary actions of certain torsion-free hyperbolic groups / Author of the conference Geffen, Shirly.
Bibliography
- ARICI, Francesca, GERONTOGIANNIS, Dimitris Michail, et NESHVEYEV, Sergey. KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems. arXiv preprint arXiv:2401.01725, 2024. - https://arxiv.org/abs/2401.01725
- ARICI, Francesca et KAAD, Jens. Gysin sequences and SU (2)‐symmetries of C∗‐algebras. Transactions of the London Mathematical Society, 2021, vol. 8, no 1, p. 440-492. - https://doi.org/10.1112/tlm3.12038
- ARICI, Francesca, KAAD, Jens, et LANDI, Giovanni. Pimsner algebras and Gysin sequences from principal circle actions. Journal of Noncommutative Geometry, 2016, vol. 10, no 1, p. 29-64. - https://doi.org/10.4171/jncg/228
- HABBESTAD, Erik et NESHVEYEV, Sergey. Subproduct systems with quantum group symmetry. Journal of Noncommutative Geometry, 2023, vol. 18, no 1, p. 93-121. - https://arxiv.org/abs/2212.08512
- HABBESTAD, Erik et NESHVEYEV, Sergey. Subproduct systems with quantum group symmetry. Journal of Noncommutative Geometry, 2023, vol. 18, no 1, p. 93-121. - https://doi.org/10.4171/JNCG/523
- SHALIT, Orr et SOLEL, Baruch. Subproduct systems. Documenta Mathematica, 2009, vol. 14, p. 801-868. - https://doi.org/10.4171/DM/290
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