Irrational rotation algebra — 2 articles found.

The Surprising Power of Averaging over Groups

C. R. Math. Rep. Acad. Sci. Canada Vol. 42 (3) 2020, pp. 38-41
Vol.42 (3) 2020
James Hogan; Samuel Li Details
(Received: 2020-09-20 )
(Received: 2020-09-20 )

James Hogan Department of Mathematics, University of Toronto, 40 St George St, Toronto, ON M5S 2E4
e-mail: james.hogan@mail.utoronto.ca

Samuel Li Department of Mathematics, University of Toronto, 40 St George St, Toronto, ON M5S 2E4
e-mail: samuelj.li@mail.utoronto.ca

Abstract/Résumé:

We highlight the surprising power of averaging via a few illuminating examples. Two of these problems involve characterizations of Hilbert space, and the third is a fundamental result in noncommutative geometry.

Nous soulignons le pouvoir surprenant de la moyenne par quelques exemples éclairants. Deux de ces problèmes concernent la caractérisation de l’espace de Hilbert, et le troisième est un résultat fondamental en géométrie non commutative.

Keywords: Averaging, Hilbert space, Irrational rotation algebra, noncommutative geometry

AMS Subject Classification: Instructional exposition (textbooks; tutorial papers; etc.), Characterizations of Hilbert spaces, Noncommutative geometry (__ la Connes) 00-01, 46C15, 58B34

PDF(click to download): The Surprising Power of Averaging over Groups

The Rieffel Projection Via Groupoids

C. R. Math. Rep. Acad. Sci. Canada Vol. 40 (2) 2018, pp. 55-60
Vol.40 (2) 2018
George A. Elliott; Dickson Wong Details
(Received: 2018-05-05 , Revised: 2018-05-05 )
(Received: 2018-05-05 , Revised: 2018-05-05 )

George A. Elliott,Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4; e-mail: elliott@math.toronto.edu

Dickson Wong,Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4; e-mail: dickson.wong@mail.utoronto.ca

Abstract/Résumé:

An elementary groupoid construction is shown to underlie Rieffel’s Hilbert module construction of a non-trivial projection in the irrational rotation C*-algebra.

Une construction élémentaire de groupoïde se révèle à la base de la construction de Rieffel à module de Hilbert d’un projecteur non-trivial dans la C*-algèbre d’une rotation irrationnelle.

Keywords: Irrational rotation algebra, Rieffel projection, groupoid construction

AMS Subject Classification: General theory of $C^*$-algebras, K-theory and operator algebras -including cyclic theory, Noncommutative topology 46L05, 46L80, 46L85

PDF(click to download): The Rieffel Projection Via Groupoids