Séminaires : Séminaire Général de Logique

Equipe(s) : lm,
Responsables :S. Anscombe, A. Khélif, A. Vignati
Email des responsables : sylvy.anscombe@imj-prg.fr, vignati@imj-prg.fr
Salle : 1013
Adresse :Sophie Germain

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Orateur(s) Andrea Vaccaro - IMJ-PRG,
Titre Set Theory and the Endomorphisms of the Calkin algebra
Horaire16:00 à 17:15
Diffusion https://u-paris.zoom.us/rec/share/ZGyJpJmh5MxufdHf1lttMLTNqXInprrWXxuOmUXK0YJaxHbAmfre-rvCA_WdHcTB.DXb1v5PMbzH6TLE_
RésumeSet theory induces a sharp dichotomy in the structure of the set of automorphisms of the Calkin algebra Q(H): under the Open Coloring Axiom (OCA) all the automorphisms of Q(H) are inner (Farah, 2011), whereas the Continuum Hypothesis (CH) implies that there exist uncountably many outer automorphisms of Q(H) (Phillips-Weaver, 2007). After a brief introduction on the line of research that led to these results, I'll discuss how this dichotomic behavior extends to the semigroup End(Q(H)) of unital endomorphisms of Q(H). In particular, we'll see that under OCA all unital endomorphisms of Q(H) can be, up to unitary equivalence, lifted to unital endomorphisms of B(H). This fact allows to have an extremely clean picture of End(Q(H)), and has some interesting consequences concerning the class of C*-algebras that embed into Q(H). I will also discuss how the structure of End(Q(H)) completely changes under CH.
AdresseSophie Germain