Semigroup C∗-algebras generated by isometric representations for free products of rational number semigroups
https://doi.org/10.26907/2949-3919.2026.2.86-103
Abstract
We study the reduced semigroup C∗-algebras generated by the left regular representations of free products for countable families of rational number semigroups. It is shown that these algebras are nuclear and amenable. We give their characterization as universal C∗-algebras determined by generators subject to polynomial relations.
Keywords
amenable C∗-algebra,
free product of semigroups,
inductive sequence,
left amenable semigroup,
nuclear C∗-algebra,
semigroup C∗-algebra,
universal C∗-algebra
Supporting agencies: The work is supported by the grant of the Russian Science Foundation and the State institution “Tatarstan Academy of Sciences”, project no. 24-21-20112, https://rscf.ru/en/project/24-21-20112/.
About the Authors
R. N. Gumerov
Kazan Federal University, N.I.Lobachevsky Institute of Mathematics and Mechanics
Russian Federation
Russian Federation
Renat Nelsonovich Gumerov,
35, Kremlyovskaya str., Kazan 420008.
E. V. Lipacheva
Kazan State Power Engineering University
Russian Federation
Russian Federation
Ekaterina Vladimirovna Lipacheva,
51, Krasnoselskaya str., Kazan 420066.
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For citations:
Gumerov R.N., Lipacheva E.V. Semigroup C∗-algebras generated by isometric representations for free products of rational number semigroups. Mathematics and Theoretical Computer Science. 2026;4(2):86-103. (In Russ.) https://doi.org/10.26907/2949-3919.2026.2.86-103
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