Spheres, Euler classes and the K-theory of C²-algebras of subproduct systems | Vidéo | Carmin.tv

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Spheres, Euler classes and the K-theory of C²-algebras of subproduct systems

By Francesca Arici

Appears in collection : Group operator algebras and Non commutative geometry / Algèbres d'opérateurs de groupes et Geometrie non commutative

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 C²-algebras in this class satisfy KK-theoretic Poincaré duality.

Information about the video

Date of recording 23/04/2024
Date of publication 13/05/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20165403
Cite this video Arici, Francesca (23/04/2024). Spheres, Euler classes and the K-theory of C²-algebras of subproduct systems. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20165403
URL https://dx.doi.org/10.24350/CIRM.V.20165403

Domain(s)

Operator Algebras

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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