KFU. Card publication. Gumerov R., Lipacheva E., Grigoryan T., On a topology and limits for inductive systems of $C^*$-algebras over partially ordered sets

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GUMEROV R., LIPACHEVA E., GRIGORYAN T., ON A TOPOLOGY AND LIMITS FOR INDUCTIVE SYSTEMS OF $C^*$-ALGEBRAS OVER PARTIALLY ORDERED SETS

Form of presentation

Articles in international journals and collections

Year of publication

2018

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Authors, employees of KFU

Gumerov Renat Nelsonovich, author

Bibliographic description in the original language

Gumerov R., Lipacheva E., Grigoryan T., On a topology and limits for inductive systems of $C^*$-algebras over partially ordered sets//http://arxiv.org/abs/1811.01234

Annotation

Motivated by algebraic quantum field theory and our previous work we study properties of inductive systems of \ $C^*$-algebras over arbitrary partially ordered sets. A partially ordered set can be represented as the union of the family of its maximal upward directed subsets indexed by elements of a certain set. We consider a topology on the set of indices generated by a base of neighbourhoods. Examples of those topologies with different properties are given. An inductive system of $C^*$-algebras and its inductive limit arise naturally over each maximal upward directed subset. Using those inductive limits, we construct different types of $C^*$-algebras. In particular, for neighbourhoods of the topology on the set of indices we deal with the $C^*$-algebras which are the direct products of those inductive limits. The present paper is concerned with the above-mentioned topology and the algebras arising from an inductive system of $C^*$-algebras over a partially ordered set.

Keywords

$C^*$-algebra, Inductive system

The name of the journal

arXiv.org

URL

http://arxiv.org/abs/1811.01234

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

https://repository.kpfu.ru/eng/?p_id=188062&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Gumerov Renat Nelsonovich	ru_RU
dc.date.accessioned	2018-01-01T00:00:00Z	ru_RU
dc.date.available	2018-01-01T00:00:00Z	ru_RU
dc.date.issued	2018	ru_RU
dc.identifier.citation	Gumerov R., Lipacheva E., Grigoryan T., On a topology and limits for inductive systems of $C^*$-algebras over partially ordered sets//http://arxiv.org/abs/1811.01234	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=188062&p_lang=2	ru_RU
dc.description.abstract	arXiv.org	ru_RU
dc.description.abstract	Motivated by algebraic quantum field theory and our previous work we study properties of inductive systems of \ $C^$-algebras over arbitrary partially ordered sets. A partially ordered set can be represented as the union of the family of its maximal upward directed subsets indexed by elements of a certain set. We consider a topology on the set of indices generated by a base of neighbourhoods. Examples of those topologies with different properties are given. An inductive system of $C^$-algebras and its inductive limit arise naturally over each maximal upward directed subset. Using those inductive limits, we construct different types of $C^$-algebras. In particular, for neighbourhoods of the topology on the set of indices we deal with the $C^$-algebras which are the direct products of those inductive limits. The present paper is concerned with the above-mentioned topology and the algebras arising from an inductive system of $C^*$-algebras over a partially ordered set.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	$C^*$-algebra	ru_RU
dc.subject	Inductive system	ru_RU
dc.title	Gumerov R., Lipacheva E., Grigoryan T., On a topology and limits for inductive systems of $C^*$-algebras over partially ordered sets	ru_RU
dc.type	Articles in international journals and collections	ru_RU