Казанский (Приволжский) федеральный университет, КФУ
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INDUCTIVE SYSTEMS OF C*-ALGEBRAS OVER POSETS: A SURVEY.
Форма представленияСтатьи в российских журналах и сборниках
Год публикации2020
Языканглийский
  • 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
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