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Уфимский математический журнал, 2024, том 16, выпуск 3, страницы 118–129
(Mi ufa700)
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Categorical criterion for existence of universal $C^*$–algebras
R. N. Gumerova, E. V. Lipachevaab, K. A. Shishkina a Lobachevskii Institute of Mathematics and Mechanics,
Kazan (Volga Region) Federal University,
Kremlevskaya str. 35,
420008, Kazan, Russia
b Chair of Higher Mathematics, Kazan State Power Engineering University,
Krasnoselskaya str. 51, 420066, Kazan, Russia
Аннотация:
We deal with categories, which determine universal $C^*$–algebras. These categories are called the compact $C^*$–relations. They were introduced by T.A. Loring. Given a set $X,$ a compact $C^*$–relation on $X$ is a category, the objects of which are functions from $X$ to $C^*$–algebras, and morphisms are $\ast$–homomorphisms of $C^*$–algebras making the appropriate triangle diagrams commute. Moreover, these functions and $\ast$–homomorphisms satisfy certain axioms. In this article, we prove that every compact $C^*$–relation is both complete and cocomplete. As an application of the completeness of compact $C^*$–relations, we obtain the criterion for the existence of universal $C^*$–algebras.
Ключевые слова:
compact $C^*$–relation, complete category, universal $C^*$–algebra.
Поступила в редакцию: 03.11.2023
Образец цитирования:
R. N. Gumerov, E. V. Lipacheva, K. A. Shishkin, “Categorical criterion for existence of universal $C^*$–algebras”, Уфимск. матем. журн., 16:3 (2024), 118–129; Ufa Math. J., 16:3 (2024), 113–124
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/ufa700 https://www.mathnet.ru/rus/ufa/v16/i3/p118
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