Geodesic
On a class of local groups and their representations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2022), pp. 76-82

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In the work the authors propose to apply the notion of a local group in the theory of $C^*$-algebras. The regular representation is defined, which is a $*$-representation and generates the reduced $C^*$-algebra. A class of local groups is constructed, generated by the subset $P$ of a discrete group, for which the notion of the $P$-regular representation is defined, which is a strong $*$-representation and generates the corresponding reduced algebra. Examples of simple algebras are given, constructed from given subsets of an abelian group.
Keywords: local group, partial isometry, regular representation, graded $C^*$-algebra, $UHF$-algebra, $AF$-algebra. 
@article{IVM_2022_2_a5,
     author = {S. A. Grigoryan and A. Yu. Kuznetsova},
     title = {On a class of local groups and their representations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--82},
     publisher = {mathdoc},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_2_a5/}
}
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S. A. Grigoryan; A. Yu. Kuznetsova. On a class of local groups and their representations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2022), pp. 76-82. http://geodesic.mathdoc.fr/item/IVM_2022_2_a5/