matatecsМатематика и теоретические компьютерные наукиMathematics and Theoretical Computer Science2949-3919Казанский (Приволжский) федеральный университет10.26907/2949-3919.2026.2.86-103matatecs-111Research ArticleСТАТЬИПолугрупповые C∗-алгебры, порожденные изометрическими представлениями свободных произведений полугрупп рациональных чиселSemigroup C∗-algebras generated by isometric representations for free products of rational number semigroupsГумеровР. Н.GumerovR. N.

Ренат Нельсонович Гумеров,

ул. Кремлевская, д. 18, г. Казань, 420008.

Renat Nelsonovich Gumerov,

35, Kremlyovskaya str., Kazan 420008.

Renat.Gumerov@kpfu.ruЛипачеваЕ. В.LipachevaE. V.

Екатерина Владимировна Липачева,

ул. Красносельская, д. 51, г. Казань, 420066.

Ekaterina Vladimirovna Lipacheva,

51, Krasnoselskaya str., Kazan 420066.

elipacheva@gmail.comКазанский (Приволжский) федеральный университет, Институт математики и механики им. Н.И. ЛобачевскогоРоссияKazan Federal University, N.I.Lobachevsky Institute of Mathematics and MechanicsRussian FederationКазанский государственный энергетический университетРоссияKazan State Power Engineering UniversityRussian Federation2026290720264286103Copyright © Гумеров Р.Н., Липачева Е.В., 20262026Гумеров Р.Н., Липачева Е.В.Gumerov R.N., Lipacheva E.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://matatecs.elpub.ru/jour/article/view/111

Рассматриваются приведенные полугрупповые C∗-алгебры, порожденные левыми регулярными изометрическими представлениями свободных произведений счетных семейств полугрупп рациональных чисел. Показывается, что эти алгебры являются ядерными и аменабельными. Получена их характеризация в качестве универсальных C∗-алгебр, задаваемых множествами порождающих элементов, удовлетворяющих полиномиальным соотношениям.

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.

аменабельная C∗-алгебраиндуктивная последовательностьлевоаменабельная полугруппаполугрупповая C∗-алгебрасвободное произведение полугруппуниверсальная C∗-алгебраядерная C∗-алгебраamenable C∗-algebrafree product of semigroupsinductive sequenceleft amenable semigroupnuclear C∗-algebrasemigroup C∗-algebrauniversal C∗-algebraИсследование выполнено за счет гранта Российского научного фонда и Академии наук Республики Татарстан по проекту №24-21-20112, https://www.rscf.ru/project/24-21-20112/.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/.ReferencesX.Li, Semigroup C∗-algebras, in: K-theory for group C∗-algebras and semigroup C∗-algebras, Oberwolfach Seminars 47, Birkh¨auser, Cham, 167–272 (2017). https://doi.org/10.1007/978-3-319-59915-1_5X.Li, Semigroup C∗-algebras, in: K-theory for group C∗-algebras and semigroup C∗-algebras, Oberwolfach Seminars 47, Birkhäuser, Cham, 167–272 (2017). https://doi.org/10.1007/978-3-319-59915-1_5R.Gumerov, A.Kuklin, E.Lipacheva, A universal property of semigroup C∗-algebras generated by cones in groups of rationals, Ann. 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The authors declare that there are no conflicts of interest present.