Geodesic
On Graded Semigroup $C^*$-Algebras and Hilbert Modules
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 131-142

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Reduced semigroup $C^*$-algebras for arbitrary cancellative semigroups are studied. It is proved that if there exists a semigroup epimorphism from a semigroup to an arbitrary group $G$, then the corresponding semigroup $C^*$-algebra is topologically $G$-graded. It is also demonstrated that if the group is finite, then the graded semigroup $C^*$-algebra has the structure of a projective Hilbert $C^*$-module. 
@article{TM_2021_313_a11,
     author = {E. V. Lipacheva},
     title = {On {Graded} {Semigroup} $C^*${-Algebras} and {Hilbert} {Modules}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {131--142},
     publisher = {mathdoc},
     volume = {313},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_313_a11/}
}
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E. V. Lipacheva. On Graded Semigroup $C^*$-Algebras and Hilbert Modules. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 131-142. http://geodesic.mathdoc.fr/item/TM_2021_313_a11/