{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:20Z","timestamp":1740134540268,"version":"3.37.3"},"reference-count":23,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,10,19]],"date-time":"2020-10-19T00:00:00Z","timestamp":1603065600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004054","name":"King Abdulaziz University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004054","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2020,10,19]]},"abstract":"<jats:p>The relationship between JW-algebras (resp. JC-algebras) and their universal enveloping von Neumann algebras (resp. <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:msup>\n                           <a:mrow>\n                              <a:mi>C<\/a:mi>\n                           <\/a:mrow>\n                           <a:mrow>\n                              <a:mi>\u2217<\/a:mi>\n                           <\/a:mrow>\n                        <\/a:msup>\n                     <\/a:math>\n                  <\/jats:inline-formula>-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 <jats:inline-formula>\n                     <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <c:msup>\n                           <c:mrow>\n                              <c:mi>C<\/c:mi>\n                           <\/c:mrow>\n                           <c:mrow>\n                              <c:mi>\u2217<\/c:mi>\n                           <\/c:mrow>\n                        <\/c:msup>\n                     <\/c:math>\n                  <\/jats:inline-formula>-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.<\/jats:p>","DOI":"10.1155\/2020\/6976084","type":"journal-article","created":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T07:55:00Z","timestamp":1603526100000},"page":"1-7","source":"Crossref","is-referenced-by-count":0,"title":["On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5596-1050","authenticated-orcid":true,"given":"F. B. H.","family":"Jamjoom","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King AbdulAziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. H.","family":"Al Otaibi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King AbdulAziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"volume-title":"Fundamentals of the Theory of Operator Algebras I","year":"1983","author":"R. V. Kadison","key":"1"},{"key":"2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6188-9","volume-title":"Theory of Operator Algebras I","author":"M. Takesaki","year":"1979"},{"volume-title":"C\u2217-algebras and Their Automorphism Groups","year":"1979","author":"G. K. Pedersen","key":"3"},{"volume-title":"Jordan Operator Algebras","year":"1984","author":"H. Hanche-Olsen","key":"4"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/45.1.77"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.4153\/cjm-1983-059-8"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-16.3.507"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1017\/s0305004100071255"},{"key":"9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0147-2","volume-title":"State Spaces of Operator Algebras","author":"E. M. Alfsen","year":"2001"},{"key":"10","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0019-2","volume-title":"Geometry of State Spaces of Operator Algebras","author":"E. M. Alfsen","year":"2003"},{"key":"11","first-page":"313","article-title":"Jordan algebras of self-adjoint operators","volume":"31","author":"E. G. Effros","year":"1965","journal-title":"Journal of the American Mathematical Society"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/bf02392126"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/bf01214723"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/34.1.7"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1307\/mmj\/1029004996"},{"key":"16","first-page":"119","article-title":"On the universal enveloping von Neumann algebra of an atomic JW-algebra","volume":"13","author":"F. B. H. Jamjoom","year":"1998","journal-title":"Journal of Natural Geometry"},{"key":"17","first-page":"267","article-title":"Injective JW-algebras","volume":"47","author":"F. B. H. Jamjoom","year":"2007","journal-title":"Kyungpook Mathematical Journal"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.2307\/1994536"},{"volume-title":"Fundamentals of the Theory of Operator Algebras II","year":"1986","author":"R. V. Kadison","key":"19"},{"volume-title":"Lectures on Von Neumann Algebras","year":"1979","author":"S. Stratila","key":"20"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.2307\/1994779"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.4153\/cjm-1995-040-1"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-19.2.335"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2020\/6976084.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2020\/6976084.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2020\/6976084.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T07:55:06Z","timestamp":1603526106000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ijmms\/2020\/6976084\/"}},"subtitle":[],"editor":[{"given":"Irena","family":"Lasiecka","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2020,10,19]]},"references-count":23,"alternative-id":["6976084","6976084"],"URL":"https:\/\/doi.org\/10.1155\/2020\/6976084","relation":{},"ISSN":["1687-0425","0161-1712"],"issn-type":[{"type":"electronic","value":"1687-0425"},{"type":"print","value":"0161-1712"}],"subject":[],"published":{"date-parts":[[2020,10,19]]}}}