Geodesic
Grading of a semigroup $C^*$-algebra by a local group
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 85-90.

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

In this paper we consider the grading by a local group of the semigroup $C^\ast$-algebra generated by the free product of abelian semigroups. The simplest of these algebras is the Cuntz-Toeplitz algebra $TO_n$. For such algebras, an abstract version of the Fourier series by the local group is constructed. A number of properties of the "harmonics" of this series are given.
Keywords: semigroup $C^\ast$-algebra, local group, Fell bundle, partial representation. 
@article{IVM_2023_7_a8,
     author = {S. A. Grigoryan and A. Sh. Sharafutdinov},
     title = {Grading of a semigroup $C^*$-algebra by a local group},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {85--90},
     publisher = {mathdoc},
     number = {7},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_7_a8/}
}
TY  - JOUR
AU  - S. A. Grigoryan
AU  - A. Sh. Sharafutdinov
TI  - Grading of a semigroup $C^*$-algebra by a local group
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 85
EP  - 90
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_7_a8/
LA  - ru
ID  - IVM_2023_7_a8
ER  - 
%0 Journal Article
%A S. A. Grigoryan
%A A. Sh. Sharafutdinov
%T Grading of a semigroup $C^*$-algebra by a local group
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 85-90
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_7_a8/
%G ru
%F IVM_2023_7_a8
S. A. Grigoryan; A. Sh. Sharafutdinov. Grading of a semigroup $C^*$-algebra by a local group. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 85-90. http://geodesic.mathdoc.fr/item/IVM_2023_7_a8/

[1] Grigoryan S.A., Gumerov R.N., Lipacheva E.V., “Predely induktivnykh posledovatelnostei algebr Teplitsa-Kuntsa”, Matematika kvantovykh tekhnologii, Tr. MIAN, 313, MIAN, M., 2021, 67–77 | DOI

[2] Exel R., Partial Dynamical Systems, Fell Bundles and Applications, Mathematical surveys and monographs, 224, Amer. Math. Soc., Providence, Rhode Island, 2017 | DOI | MR | Zbl

[3] Pontryagin L.S., Nepreryvnye gruppy, GONTI NKTP SSSR, M., 1938 | MR

[4] Maltsev A.I., “O lokalnykh i polnykh topologicheskikh gruppakh”, Izbrannye trudy, v. 1, eds. Aleksandrov P.S. i dr., Nauka, M., 1976

[5] Grigoryan S.A., Kuznetsova A.Yu., “On a Grading of the Cuntz Algebra”, Lobachevskii Journal of Mathematics, 40:10 (2019), 1479–1482 | DOI | MR | Zbl

[6] Grigoryan S.A., Kuznetsova A.Yu., “Lokalnye gruppy i ikh predstavleniya”, Izv. vuzov. Matem., 2020, no. 6, 73–78 | Zbl

[7] Grigoryan S.A., Kuznetsova A.Yu., “Ob odnom klasse lokalnykh grupp i ikh predstavlenii”, Izv. vuzov. Matem., 2022, no. 2, 76–82 | Zbl