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. 
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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/

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