Seminar

Language English
From 2012/01/11 16:30
To 2012/01/11 17:30
PlaceRoom 110, RIMS, Kyoto University
Seminar NameColloquium
Title Existence of outer automorphisms of the Calkin algebra is undecidable 　
Field Algebra
Geometry
Analysis
Other
SpeakersN. Christopher Phillips
AffiliationRIMS / University of Oregon
AbstractLet be a separable infinite dimensional Hilbert space, for example, the space of all square summable sequences. Let be the algebra of all continuous linear maps from to~ and let be the closure in of the set of continuous linear maps which have finite rank. Then is an ideal in and we can form the quotient algebra It is called the Calkin algebra, and is an example of a C*-algebra. Question: Does the Calkin algebra have outer automorphisms, that is, automorphisms not of the form for suitable ?
　It turns out that this question is undecidable in ZFC. If one assumes the Continuum Hypothesis, then outer automorphisms exist. In fact, there are more automorphisms than there are possible choices for~ (This is joint work with Nik Weaver.) However, Ilijas Farah proved that it is consistent with ZFC that ~has no outer automorphisms.
　This talk is intended for a general audience. I will describe some of the background, and give several of the ideas of the proof that the Continuum Hypothesis implies the existence of outer automorphisms of the Calkin algebra.
Note16:00-16:30 1階ロビーでtea

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Linkhttp://www.kurims.kyoto-u.ac.jp/ja/seminar/danwakai.html