KFU. Card publication. Inductive Systems of C*-Algebras over Posets: A Survey.

KAZAN
FEDERAL UNIVERSITY

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INDUCTIVE SYSTEMS OF C*-ALGEBRAS OVER POSETS: A SURVEY.

Form of presentation

Articles in Russian journals and collections

Year of publication

2020

Язык

английский

Authors, employees of KFU

Gumerov Renat Nelsonovich, author

Bibliographic description in the original language

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

Annotation

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.

Keywords

inductive system

The name of the journal

Lobachevskii J. Math.

URL

https://link.springer.com/article/10.1134/S1995080220040137

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=236808&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Gumerov Renat Nelsonovich	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/eng/?p_id=236808&p_lang=2	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	Articles in Russian journals and collections	ru_RU