Geodesic
Grading of a semigroup $C^*$-algebra by a local group
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 85-90 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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