セミナー

発表言語 英語
開催日 2012年01月11日 16時30分
終了日 2012年01月11日 17時30分
開催場所京都大学数理解析研究所110号室
セミナー名談話会
タイトル Existence of outer automorphisms of the Calkin algebra is undecidable  
分野 代数
幾何
解析
その他
講演者名N. Christopher Phillips
講演者所属RIMS / University of Oregon
概要Let 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.
備考16:00-16:30 1階ロビーでtea

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