| Форма представления | Статьи в российских журналах и сборниках |
| Год публикации | 2020 |
| Язык | английский |
|
Гумеров Ренат Нельсонович, автор
|
| Библиографическое описание на языке оригинала |
Gumerov, R.N., Lipacheva, E.V. Inductive Systems of C*-Algebras over Posets: A Survey. Lobachevskii J Math 41, 644–654 (2020). https://doi.org/10.1134/S1995080220040137 |
| Аннотация |
We survey the research on the inductive systems of C^{*}-algebras over arbitrary partially ordered sets. The motivation for our work comes from the theory of reduced semigroup C^{*}-algebras and local quantum field theory. We study the inductive limits for the inductive systems of Toeplitz algebras over directed sets. The connecting \ast-homomorphisms of such systems are defined by sets of natural numbers satisfying some coherent property. These inductive limits coincide up to isomorphisms with the reduced semigroup C^{*}-algebras for the semigroups of non-negative rational numbers. By Zorn's lemma, every partially ordered set K is the union of the family of its maximal directed subsets K_{i} indexed by elements of a set I. For a given inductive system of C^{*}-algebras over K one can construct the inductive subsystems over K_{i} and the inductive limits for these subsystems. We consider a topology on the set I. It is shown that characteristics of this topology are closely related to properties of the limits for the inductive subsystems. |
| Ключевые слова |
inductive system |
| Название журнала |
Lobachevskii J. Math.
|
| URL |
https://link.springer.com/article/10.1134/S1995080220040137 |
| Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку |
https://repository.kpfu.ru/?p_id=236808 |
Полная запись метаданных  |
| Поле DC |
Значение |
Язык |
| dc.contributor.author |
Гумеров Ренат Нельсонович |
ru_RU |
| dc.date.accessioned |
2020-01-01T00:00:00Z |
ru_RU |
| dc.date.available |
2020-01-01T00:00:00Z |
ru_RU |
| dc.date.issued |
2020 |
ru_RU |
| dc.identifier.citation |
Gumerov, R.N., Lipacheva, E.V. Inductive Systems of C*-Algebras over Posets: A Survey. Lobachevskii J Math 41, 644–654 (2020). https://doi.org/10.1134/S1995080220040137 |
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/?p_id=236808 |
ru_RU |
| dc.description.abstract |
Lobachevskii J. Math. |
ru_RU |
| dc.description.abstract |
We survey the research on the inductive systems of C^{*}-algebras over arbitrary partially ordered sets. The motivation for our work comes from the theory of reduced semigroup C^{*}-algebras and local quantum field theory. We study the inductive limits for the inductive systems of Toeplitz algebras over directed sets. The connecting \ast-homomorphisms of such systems are defined by sets of natural numbers satisfying some coherent property. These inductive limits coincide up to isomorphisms with the reduced semigroup C^{*}-algebras for the semigroups of non-negative rational numbers. By Zorn's lemma, every partially ordered set K is the union of the family of its maximal directed subsets K_{i} indexed by elements of a set I. For a given inductive system of C^{*}-algebras over K one can construct the inductive subsystems over K_{i} and the inductive limits for these subsystems. We consider a topology on the set I. It is shown that characteristics of this topology are closely related to properties of the limits for the inductive subsystems. |
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
|
ru_RU |
| dc.title |
Inductive Systems of C*-Algebras over Posets: A Survey. |
ru_RU |
| dc.type |
Статьи в российских журналах и сборниках |
ru_RU |
|
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