Geodesic
$C^*$-algebras generated by mappings. Criterion of irreducibility
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 10-22

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

We study the operator algebra associated with a self-mapping $\varphi $ on a countable set $ X $ which can be represented as a directed graph. The algebra is generated by the family of partial isometries acting on the corresponding $ l^ 2(X) $. We study the structure of involutive semigroup multiplicatively generated by the family of partial isometries. We formulate the criterion when the algebra is irreducible on the Hilbert space. We consider the concrete examples of operator algebras. In particular, we give the examples of nonisomorphic $C^*$-algebras, which are the extensions by compact operators of the algebra of continuous functions on the unit circle.
Keywords: $C^*$-algebra, partial isometry, positive operator, projection, compact operator, Toeplitz algebra, extension of $C^*$-algebra by compact operators. 
@article{IVM_2018_2_a1,
     author = {S. A. Grigoryan and A. Yu. Kuznetsova},
     title = {$C^*$-algebras generated by mappings. {Criterion} of irreducibility},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {10--22},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_2_a1/}
}
TY  - JOUR
AU  - S. A. Grigoryan
AU  - A. Yu. Kuznetsova
TI  - $C^*$-algebras generated by mappings. Criterion of irreducibility
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 10
EP  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_2_a1/
LA  - ru
ID  - IVM_2018_2_a1
ER  - 
%0 Journal Article
%A S. A. Grigoryan
%A A. Yu. Kuznetsova
%T $C^*$-algebras generated by mappings. Criterion of irreducibility
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 10-22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2018_2_a1/
%G ru
%F IVM_2018_2_a1
S. A. Grigoryan; A. Yu. Kuznetsova. $C^*$-algebras generated by mappings. Criterion of irreducibility. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 10-22. http://geodesic.mathdoc.fr/item/IVM_2018_2_a1/