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The corresponding axial algebras are called [Formula: see text]-axial algebras, where [Formula: see text] is an element of the ground field. As a first step toward their classification, we describe the 2- and 3-generated subalgebras of such algebras. <\/jats:p>","DOI":"10.1142\/s0218196724500383","type":"journal-article","created":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T06:05:46Z","timestamp":1720159546000},"page":"937-960","source":"Crossref","is-referenced-by-count":0,"title":["Axial view on pseudo-composition algebras and train algebras of rank 3"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6239-2092","authenticated-orcid":false,"given":"Ilya","family":"Gorshkov","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics, Novosibirsk, Russia"},{"name":"Saint Petersburg State University, Saint Petersburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0324-5287","authenticated-orcid":false,"given":"Andrey","family":"Mamontov","sequence":"additional","affiliation":[{"name":"Sobolev Institute of Mathematics, Novosibirsk, Russia"},{"name":"Saint Petersburg State University, Saint Petersburg, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3914-6758","authenticated-orcid":false,"given":"Alexey","family":"Staroletov","sequence":"additional","affiliation":[{"name":"Sobolev Institute of Mathematics, Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,8,3]]},"reference":[{"key":"S0218196724500383BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s002090000151"},{"key":"S0218196724500383BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/S0370164600012323"},{"key":"S0218196724500383BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389186"},{"key":"S0218196724500383BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2014.08.035"},{"key":"S0218196724500383BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2015.03.026"},{"key":"S0218196724500383BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-017-1615-7"},{"issue":"4","key":"S0218196724500383BIB007","first-page":"397","volume":"13","author":"Hall J. 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