{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T07:08:11Z","timestamp":1774595291582,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"accepted":{"date-parts":[[2024,1,5]]},"published-print":{"date-parts":[[2024,2,14]]},"abstract":"<jats:p>\n                    We describe transposed Poisson structures on the upper triangular matrix Lie algebra\n                    <jats:inline-formula>\n                      <jats:tex-math>T_{n}(F)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:inline-formula>\n                      <jats:tex-math>n&gt;1<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , over a field\n                    <jats:inline-formula>\n                      <jats:tex-math>F<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    of characteristic zero. We prove that, for\n                    <jats:inline-formula>\n                      <jats:tex-math>n&gt;2<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , any such structure is either of Poisson type or the orthogonal sum of a fixed non-Poisson structure with a structure of Poisson type, and for\n                    <jats:inline-formula>\n                      <jats:tex-math>n=2<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , there is one more class of transposed Poisson structures on\n                    <jats:inline-formula>\n                      <jats:tex-math>T_{n}(F)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . We also show that, up to isomorphism, the full matrix Lie algebra\n                    <jats:inline-formula>\n                      <jats:tex-math>M_{n}(F)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    admits only one non-trivial transposed Poisson structure, and it is of Poisson type.\n                  <\/jats:p>","DOI":"10.4171\/pm\/2120","type":"journal-article","created":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T17:45:12Z","timestamp":1707932712000},"page":"135-149","source":"Crossref","is-referenced-by-count":4,"title":["Transposed Poisson structures on the Lie algebra of upper triangular matrices"],"prefix":"10.4171","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2084-9215","authenticated-orcid":false,"given":"Ivan","family":"Kaygorodov","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03nf36p02","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade da Beira Interior, Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4504-3261","authenticated-orcid":false,"given":"Mykola","family":"Khrypchenko","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041akq887","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade Federal de Santa Catarina, Florian\u00f3polis, Brazil"},{"id":[{"id":"https:\/\/ror.org\/043pwc612","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade do Porto, Porto, Portugal"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"deposited":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T12:05:46Z","timestamp":1761825946000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/2120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,14]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.4171\/pm\/2120","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"value":"0032-5155","type":"print"},{"value":"1662-2758","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,14]]}}}