RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

 Mat. Sb., 1999, Volume 190, Number 2, Pages 3–30 (Mi msb381)

On the homotopy equivalence of simple AI-algebras

O. Yu. Aristov

Obninsk State Technical University for Nuclear Power Engineering

Abstract: Let $A$ and $B$ be simple unital AI-algebras (an AI-algebra is an inductive limit of $C^*$-algebras of the form $\bigoplus_i^kC([0,1],M_{N_i})$. It is proved that two arbitrary unital homomorphisms from $A$ into $B$ such that the corresponding maps $\mathrm K_0A\to\mathrm K_0B$ coincide are homotopic. Necessary and sufficient conditions on the Elliott invariant for $A$ and $B$ to be homotopy equivalent are indicated. Moreover, two algebras in the above class having the same $\mathrm K$-theory but not homotopy equivalent are constructed. A theorem on the homotopy of approximately unitarily equivalent homomorphisms between AI-algebras is used in the proof, which is deduced in its turn from a generalization to the case of AI-algebras of a theorem of Manuilov stating that a unitary matrix almost commuting with a self-adjoint matrix $h$ can be joined to 1 by a continuous path consisting of unitary matrices almost commuting with $h$.

DOI: https://doi.org/10.4213/sm381

Full text: PDF file (406 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 1999, 190:2, 165–191

Bibliographic databases:

UDC: 517.986.32
MSC: Primary 46L85, 58B30; Secondary 46L89

Citation: O. Yu. Aristov, “On the homotopy equivalence of simple AI-algebras”, Mat. Sb., 190:2 (1999), 3–30; Sb. Math., 190:2 (1999), 165–191

Citation in format AMSBIB
\Bibitem{Ari99} \by O.~Yu.~Aristov \paper On the homotopy equivalence of simple AI-algebras \jour Mat. Sb. \yr 1999 \vol 190 \issue 2 \pages 3--30 \mathnet{http://mi.mathnet.ru/msb381} \crossref{https://doi.org/10.4213/sm381} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1700998} \zmath{https://zbmath.org/?q=an:0942.46043} \transl \jour Sb. Math. \yr 1999 \vol 190 \issue 2 \pages 165--191 \crossref{https://doi.org/10.1070/sm1999v190n02ABEH000381} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000081091800006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0033246625} 

• http://mi.mathnet.ru/eng/msb381
• https://doi.org/10.4213/sm381
• http://mi.mathnet.ru/eng/msb/v190/i2/p3

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Korchagin A.I., “Topological Complexity of Certain Classes of $C^*$-Algebras”, Russ. J. Math. Phys., 24:3 (2017), 347–353
•  Number of views: This page: 186 Full text: 82 References: 22 First page: 1