{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:44:34Z","timestamp":1740120274342,"version":"3.37.3"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["17-11-01124"],"award-info":[{"award-number":["17-11-01124"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:p> We consider zero divisors of an arbitrary real Cayley\u2013Dickson algebra such that their components are both standard basis elements. We construct inductively the orthogonality graph on these elements. Then we show that, if we restrict our attention to at least [Formula: see text]-dimensional algebras, two algebras are isomorphic if and only if their graphs are isomorphic. We also provide an algorithm to retrieve the Cayley\u2013Dickson parameters of an algebra from its graph. <\/jats:p>","DOI":"10.1142\/s0218196721500338","type":"journal-article","created":{"date-parts":[[2021,5,15]],"date-time":"2021-05-15T16:11:36Z","timestamp":1621095096000},"page":"691-725","source":"Crossref","is-referenced-by-count":1,"title":["Orthogonality graphs of real Cayley\u2013Dickson algebras. Part II: The subgraph on pairs of basis elements"],"prefix":"10.1142","volume":"31","author":[{"given":"Svetlana","family":"Zhilina","sequence":"first","affiliation":[{"name":"Department of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow, 119991, Russia"},{"name":"Moscow Center for Fundamental and Applied, Mathematics, Moscow, 119991, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,5,12]]},"reference":[{"doi-asserted-by":"publisher","key":"S0218196721500338BIB001","DOI":"10.1090\/S0273-0979-01-00934-X"},{"doi-asserted-by":"publisher","key":"S0218196721500338BIB002","DOI":"10.1007\/s00006-018-0859-6"},{"doi-asserted-by":"publisher","key":"S0218196721500338BIB003","DOI":"10.1080\/00927870701724094"},{"issue":"2","key":"S0218196721500338BIB004","first-page":"269","volume":"13","author":"Biss D. K.","year":"2007","journal-title":"Bol. Soc. Mat. Mex."},{"doi-asserted-by":"publisher","key":"S0218196721500338BIB005","DOI":"10.4153\/CMB-2006-048-6"},{"doi-asserted-by":"publisher","key":"S0218196721500338BIB006","DOI":"10.1016\/0021-8693(90)90221-9"},{"doi-asserted-by":"publisher","key":"S0218196721500338BIB008","DOI":"10.1007\/s10958-019-04390-y"},{"volume-title":"A Taste of Jordan Algebras","year":"2004","author":"McCrimmon K.","key":"S0218196721500338BIB013"},{"issue":"1","key":"S0218196721500338BIB014","first-page":"13","volume":"4","author":"Moreno G.","year":"1998","journal-title":"Bol. Soc. Mat. Mex."},{"doi-asserted-by":"publisher","key":"S0218196721500338BIB015","DOI":"10.1142\/9789812772732_0028"},{"doi-asserted-by":"publisher","key":"S0218196721500338BIB017","DOI":"10.2307\/2372583"},{"doi-asserted-by":"publisher","key":"S0218196721500338BIB018","DOI":"10.1007\/s10958-020-04930-x"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196721500338","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,24]],"date-time":"2021-06-24T04:21:05Z","timestamp":1624508465000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196721500338"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,12]]},"references-count":12,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["10.1142\/S0218196721500338"],"URL":"https:\/\/doi.org\/10.1142\/s0218196721500338","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2021,5,12]]}}}