Geodesic
Local groups and their representations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 73-78.

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In the paper the notion of a local group is applied in the context of operator algebras, and $C^*$-algebraic constructions are proposed related to the local group. For local group we define $*$-representation and strong $*$-representation which are connected by the extension of the local group. Local group allows you to define the regular representation which is a $*$-representation, and the respective reduced $C^*$-algebra, the last is graded over the extension of the local group.
Keywords: Local group, partial isometry, group partial representation, regular representation, graded $C^*$-algebra. 
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S. A. Grigoryan; A. Yu. Kuznetsova. Local groups and their representations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 73-78. http://geodesic.mathdoc.fr/item/IVM_2020_6_a8/

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