On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras

On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras

The relationship between JW-algebras (resp. JC-algebras) and their universal enveloping von Neumann algebras (resp. C∗-algebras) can be described as significant and influential. Examples of numerous relationships have been established. In this article, we established a relationship between the set o...

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Main Authors: F. B. H. Jamjoom, A. H. Al Otaibi
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2020/6976084
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spelling doaj-0024f07cd093469a9ffb8d52ca02ac552020-11-25T03:04:32ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/69760846976084On the Relationship between Jordan Algebras and Their Universal Enveloping AlgebrasF. B. H. Jamjoom0A. H. Al Otaibi1Department of Mathematics, College of Science, King AbdulAziz University, P.O. Box 80200, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, College of Science, King AbdulAziz University, P.O. Box 80200, Jeddah 21589, Saudi ArabiaThe relationship between JW-algebras (resp. JC-algebras) and their universal enveloping von Neumann algebras (resp. C∗-algebras) can be described as significant and influential. Examples of numerous relationships have been established. In this article, we established a relationship between the set of split faces of the state space (resp. normal states) of a JC-algebra (resp. a JW-algebra) and the set of split faces of the state space (resp. normal states) of its universal enveloping C∗-algebra (resp. von Neumann algebra), and we tied up this relationship with the correspondence between the classes of invariant faces, closed ideals, and central projections of these Jordan algebras and of their universal enveloping algebras.http://dx.doi.org/10.1155/2020/6976084
collection DOAJ
language English
format Article
sources DOAJ
author F. B. H. Jamjoom
A. H. Al Otaibi
spellingShingle F. B. H. Jamjoom
A. H. Al Otaibi
On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras
International Journal of Mathematics and Mathematical Sciences
author_facet F. B. H. Jamjoom
A. H. Al Otaibi
author_sort F. B. H. Jamjoom
title On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras
title_short On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras
title_full On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras
title_fullStr On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras
title_full_unstemmed On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras
title_sort on the relationship between jordan algebras and their universal enveloping algebras
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2020-01-01
description The relationship between JW-algebras (resp. JC-algebras) and their universal enveloping von Neumann algebras (resp. C∗-algebras) can be described as significant and influential. Examples of numerous relationships have been established. In this article, we established a relationship between the set of split faces of the state space (resp. normal states) of a JC-algebra (resp. a JW-algebra) and the set of split faces of the state space (resp. normal states) of its universal enveloping C∗-algebra (resp. von Neumann algebra), and we tied up this relationship with the correspondence between the classes of invariant faces, closed ideals, and central projections of these Jordan algebras and of their universal enveloping algebras.
url http://dx.doi.org/10.1155/2020/6976084
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