Geodesic
Limits of Inductive Sequences of Toeplitz--Cuntz Algebras
Informatics and Automation, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 67-77

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We consider inductive sequences of Toeplitz–Cuntz algebras. The connecting homomorphisms of such a sequence are defined by a finite set of sequences of positive integers. We prove that the inductive limit of such a sequence of Toeplitz–Cuntz algebras is isomorphic to the reduced semigroup $C^*$-algebra constructed for the unitalization of the free product of a finite family of semigroups of positive rational numbers. We show that the limit of the inductive sequence of Toeplitz–Cuntz algebras defined by a finite set of sequences of positive integers is a simple $C^*$-algebra. 
@article{TRSPY_2021_313_a6,
     author = {S. A. Grigoryan and R. N. Gumerov and E. V. Lipacheva},
     title = {Limits of {Inductive} {Sequences} of {Toeplitz--Cuntz} {Algebras}},
     journal = {Informatics and Automation},
     pages = {67--77},
     publisher = {mathdoc},
     volume = {313},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2021_313_a6/}
}
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S. A. Grigoryan; R. N. Gumerov; E. V. Lipacheva. Limits of Inductive Sequences of Toeplitz--Cuntz Algebras. Informatics and Automation, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 67-77. http://geodesic.mathdoc.fr/item/TRSPY_2021_313_a6/