{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T09:30:45Z","timestamp":1768728645080,"version":"3.49.0"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","license":[{"start":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T00:00:00Z","timestamp":1754092800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T00:00:00Z","timestamp":1754092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100008814","name":"Universidade do Minho","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008814","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Transformation Groups"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Let <jats:italic>G<\/jats:italic> be a connected, simply connected three-dimensional Lie group (unimodular or non-unimodular) equipped with a left-invariant (Riemannian or Lorentzian) metric <jats:italic>g<\/jats:italic>. By definition, the isometry group <jats:inline-formula>\n              <jats:tex-math>$$\\textrm{Isom}(G, g)$$<\/jats:tex-math>\n            <\/jats:inline-formula> contains <jats:italic>G<\/jats:italic> itself, acting by left translations. It turns out that, generically, <jats:inline-formula>\n              <jats:tex-math>$$\\textrm{Isom}(G, g)$$<\/jats:tex-math>\n            <\/jats:inline-formula> is actually equal to <jats:italic>G<\/jats:italic>, and the natural question then becomes to classify those special metrics for which this is not the case. Using Lie-theoretical methods, we present a unified approach to obtain all pairs (<jats:italic>G<\/jats:italic>,\u00a0<jats:italic>g<\/jats:italic>) whose full isometry group <jats:inline-formula>\n              <jats:tex-math>$$\\textrm{Isom}(G, g)$$<\/jats:tex-math>\n            <\/jats:inline-formula> has dimension greater than or equal to four. As a consequence, we determine, for every pair (<jats:italic>G<\/jats:italic>,\u00a0<jats:italic>g<\/jats:italic>), up to automorphism and scaling, the dimension of <jats:inline-formula>\n              <jats:tex-math>$$\\textrm{Isom}(G, g)$$<\/jats:tex-math>\n            <\/jats:inline-formula>, which can be three, four, or six.<\/jats:p>","DOI":"10.1007\/s00031-025-09930-2","type":"journal-article","created":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T04:36:06Z","timestamp":1754109366000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Isometries of 3-Dimensional Semi-Riemannian Lie Groups"],"prefix":"10.1007","author":[{"given":"Salah","family":"Chaib","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1756-0832","authenticated-orcid":false,"given":"Ana Cristina","family":"Ferreira","sequence":"additional","affiliation":[]},{"given":"Abdelghani","family":"Zeghib","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,2]]},"reference":[{"key":"9930_CR1","doi-asserted-by":"publisher","unstructured":"Allout, S.,\u00a0Belkacem, A.,\u00a0Zeghib, A.: On homogeneous 3-dimensional spacetimes: focus on plane waves, 2023. https:\/\/doi.org\/10.48550\/arXiv.2210.11439","DOI":"10.48550\/arXiv.2210.11439"},{"key":"9930_CR2","doi-asserted-by":"publisher","unstructured":"Boucetta, M.,\u00a0Chakkar, A.: The isometry groups of Lorentzian three-dimensional unimodular simply connected Lie groups. 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