Mathematical Reports - Comptes rendus mathématiques

of the Academy of Science | de l'Académie des sciences

  • Home
  • Articles
  • News
  • Editorial Board
  • General Information
    • General Information
    • Preparation of Manuscripts
    • Subscription Information
    • FAQ
    • Help

19K14 — 4 results found.

      
Show all abstractsHide all abstracts

K-Theory and Traces
C. R. Math. Rep. Acad. Sci. Canada Vol. 44 (1) 2022, pp. 1-15
George A. Elliott (Received: 2021/09/16, Revised: 2021/12/19)

[+ show]Hide Abstract

It is shown that for a unital C*-algebra, what is sometimes referred to as the Elliott invariant—loosely speaking, K-theory and traces— i.e., the order-unit K\(_0\)-group, the K\(_1\)-group, and the trace simplex, paired in the natural way with K\(_0\), can be expressed purely in terms of K-theory, with the trace simplex and its pairing with K\(_0\) recoverable in a simple way (using polar decomposition) from algebraic K\(_1\), defined as in the purely algebraic context using invertible elements rather than just unitaries.

L’invariant naïf d’Elliott, qui est à la base de la classification complète récente d’une énorme classe de C*-algèbres simples (celles qui sont de dimension nucléaire finie, qui sont séparables, et qui satisfont à l’UCT), peut s’exprimer entièrement dans le cadre de K-théorie algébrique.

A Modification of the Effros-Handelman-Shen Theorem with $\mathbb{Z}_2$ actions
C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (3) 2021, pp. 87-102
Bit Na Choi; Andrew J. Dean (Received: 2021/04/08)

[+ show]Hide Abstract

We show that a \(\mathbb{Z}_2\) action on a lattice-ordered dimension group will arise as an inductive limit of \(\mathbb{Z}_2\) actions on simplicial groups. The motivation for this study is the range of invariant problem in Elliott and Su’s classification of AF type \(\mathbb{Z}_2\) actions. We modify the proof of the Effros-Handelman-Shen theorem to include \(\mathbb{Z}_2\) actions.

Nous montrons qu’une action de \(\mathbb{Z}_2\) sur un groupe de dimension ordonné par treillis apparaît comme une limite inductive d’actions de \(\mathbb{Z}_2\) sur des groupes simpliciaux. La motivation de cette étude est le problème de la gamme de l’invariant dans la classification d’Elliott et de Su des actions de \(\mathbb{Z}_2\) de type AF. Nous modifions la preuve du théorème d’Effros-Handelman-Shen pour inclure les actions de \(\mathbb{Z}_2\).

Dimension groups and multidimensional continued fractions
C. R. Math. Rep. Acad. Sci. Canada Vol. 33 (1) 2011, pp. 11–20
Gregory R. Maloney (Received: 2009/12/13, Revised: 2010/02/17)

Show AbstractHide Abstract

We describe a class of dimension groups associated with multidimensional continued fractions and show how a certain property of a continued fraction is reflected in the structure of its dimension group.

On décrit une classe de groupes de dimensions associés aux fractions continues multidimensionnelles et on montre comment une certaine propriété d’une fraction continue se reflète dans la structure de son groupe de dimensions.

On the irrational quartic algebra
C. R. Math. Rep. Acad. Sci. Canada Vol. 21 (3) 1999, pp. 91–96
S.G. Walters (Received: 1998/10/22)

Show AbstractHide Abstract

No abstract available but the full text is online at the title link above.

 Volume / Issue

Most used Keywords

algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

Be notified of new issues

Copyright © 2023 · The Royal Society of Canada | La Société royale du Canada · Log in
ISSN: 2816-5810 (Online)