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By hand and applying computational linear algebra on matrices, 1-identities and 2-identities of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathfrak {O}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>O<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> are established. From some of these identities, the non-conservativeness of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathfrak {O}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>O<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> and of some of its binary reduced algebras, which are binary standard composition algebras of types II and III, is proved. Also from identities of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathfrak {O}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>O<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>, using computational linear algebra based on the representation theory of the symmetric group, ternary enveloping algebras for ternary Maltsev algebras are constructed.<\/jats:p>","DOI":"10.1007\/s11785-025-01750-2","type":"journal-article","created":{"date-parts":[[2025,7,6]],"date-time":"2025-07-06T22:15:28Z","timestamp":1751840128000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On a Ternary Octonion Algebra"],"prefix":"10.1007","volume":"19","author":[{"given":"P. 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