Geodesic
$AF$-subalgebras of a~$C^*$-algebra generated by a~mapping
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 82-87.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider a $ C^*$-subalgebra of the algebra of all bounded operators $B(l^2(X))$ on the Hilbert space $l^2(X)$ with one generating element $T_\varphi$ induced by a mapping $\varphi\colon X\to X$ of the set $X$ into itself. We prove that such a $C^*$-algebra has an $AF$-subalgebra and establish commutativity conditions for the latter. We prove that a $C^*$-algebra generated by a mapping produces a dynamic system such that the corresponding group of automorphisms is invariant on elements of the $AF$-subalgebra.
Keywords: $AF$-algebra, $C^*$-algebra, partial isometry. 
@article{IVM_2010_3_a9,
     author = {S. A. Grigoryan and A. Yu. Kuznetsova},
     title = {$AF$-subalgebras of a~$C^*$-algebra generated by a~mapping},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {82--87},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_3_a9/}
}
TY  - JOUR
AU  - S. A. Grigoryan
AU  - A. Yu. Kuznetsova
TI  - $AF$-subalgebras of a~$C^*$-algebra generated by a~mapping
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 82
EP  - 87
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_3_a9/
LA  - ru
ID  - IVM_2010_3_a9
ER  - 
%0 Journal Article
%A S. A. Grigoryan
%A A. Yu. Kuznetsova
%T $AF$-subalgebras of a~$C^*$-algebra generated by a~mapping
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 82-87
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_3_a9/
%G ru
%F IVM_2010_3_a9
S. A. Grigoryan; A. Yu. Kuznetsova. $AF$-subalgebras of a~$C^*$-algebra generated by a~mapping. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 82-87. http://geodesic.mathdoc.fr/item/IVM_2010_3_a9/

[1] Grigoryan S. A., Kuznetsova A. Yu., “$C^*$-algebry, porozhdennye otobrazheniyami”, Materialy shkoly-seminara “Volga–2006”, Kazan, 2006, 28

[2] Grigoryan S., Kuznetsova A., “$C^*$-algebras generated by mappings”, Lobachevskii J. Math., 29:1 (2008), 5–8 | DOI | MR | Zbl

[3] Cuntz J., “Simple $C^*$-algebras generated by isometries”, Comm. Math. Phys., 57:2 (1977), 173–185 | DOI | MR | Zbl

[4] Kumjian A., On certain Cuntz–Pimsner algebras, , 29 Aug. 2001 arxiv: org.math/0108194v1[math.OA]

[5] Kuznetsova A. Yu., “Primery $C^*$-algebr, porozhdennykh otobrazheniyami”, Noveishie problemy teorii polya 2005–2006, Kazan, 2007, 170–175