{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:40:45Z","timestamp":1740156045018,"version":"3.37.3"},"reference-count":16,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T00:00:00Z","timestamp":1564963200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science center","award":["2018\/31\/B\/ST1\/00053"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"Let G \/ H be a homogeneous space of a compact simple classical Lie group G. Assume that the maximal torus T H of H is conjugate to a torus T \u03b2 whose Lie algebra t \u03b2 is the kernel of the maximal root \u03b2 of the root system of the complexified Lie algebra g c . We prove that such homogeneous space is formal. As an application, we give a short direct proof of the formality property of compact homogeneous 3-Sasakian spaces of classical type. This is a complement to the work of Fern\u00e1ndez, Mu\u00f1oz, and Sanchez which contains a full analysis of the formality property of S O ( 3 ) -bundles over the Wolf spaces and the proof of the formality property of homogeneous 3-Sasakian manifolds as a corollary.<\/jats:p>","DOI":"10.3390\/sym11081011","type":"journal-article","created":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T15:17:47Z","timestamp":1565018267000},"page":"1011","source":"Crossref","is-referenced-by-count":0,"title":["On Formality of Some Homogeneous Spaces"],"prefix":"10.3390","volume":"11","author":[{"given":"Aleksy","family":"Tralle","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Warmia and Mazury, S\u0142oneczna 54, 10-710 Olsztyn, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BF01389853","article-title":"Real homotopy theory of Kaehler manifolds","volume":"29","author":"Deligne","year":"1975","journal-title":"Invent. Math."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"F\u00e9lix, Y., Oprea, J., and Tanr\u00e9, D. (2008). Algebraic Models in Geometry, Oxford University Press.","DOI":"10.1093\/oso\/9780199206513.001.0001"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tralle, A., and Oprea, J. (1997). Symplectic Manifolds with no Kaehler Structure, Springer.","DOI":"10.1007\/BFb0092608"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1112\/jtopol\/jtv044","article-title":"On formality of Sasakian manifolds","volume":"9","author":"Biswas","year":"2016","journal-title":"J. Topol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1007\/s00209-012-1117-6","article-title":"Non-Formal Homogeneous Spaces","volume":"274","author":"Amann","year":"2012","journal-title":"Math. 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On SO(3)-bundles over the Wolf spaces. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1080\/00927878808823619","article-title":"Basic sets of invariant polynomials for finite reflection groups","volume":"16","author":"Mehta","year":"1988","journal-title":"Commun. Algebra"},{"key":"ref_11","unstructured":"Greub, V., Halperin, S., and Vanstone, R. (1976). Curvature, Connections and Cohomology, Academic Press."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Onishchik, A., and Vinberg, E. (1994). Lie Groups and Lie Algebras III, Springer.","DOI":"10.1007\/978-3-662-03066-0"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Boyer, C., and Galicki, K. (2007). Sasakian Geometry, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780198564959.001.0001"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"F\u00e9lix, Y., Halperin, S., and Thomas, J.-C. (2002). 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Mech."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/8\/1011\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T17:29:36Z","timestamp":1718818176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/8\/1011"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,5]]},"references-count":16,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["sym11081011"],"URL":"https:\/\/doi.org\/10.3390\/sym11081011","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,8,5]]}}}