{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T05:26:06Z","timestamp":1775539566334,"version":"3.50.1"},"reference-count":27,"publisher":"AIP Publishing","issue":"4","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,4,1]]},"abstract":"<jats:p>The present work studies deeply quadratic symplectic Lie superalgebras, obtaining, in particular, that they are all nilpotent. Consequently, we provide classifications in low dimensions and identify the double extensions that maintain symplectic structures. By means of both elementary odd double extensions and generalized double extensions of quadratic symplectic Lie superalgebras, we obtain an inductive description of quadratic symplectic Lie superalgebras of filiform type.<\/jats:p>","DOI":"10.1063\/5.0142935","type":"journal-article","created":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T11:00:55Z","timestamp":1681383655000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Quadratic symplectic Lie superalgebras with a filiform module as an odd part"],"prefix":"10.1063","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1369-3737","authenticated-orcid":false,"given":"Elisabete","family":"Barreiro","sequence":"first","affiliation":[{"name":"CMUC, Department of Mathematics, FCTUC, University of Coimbra 1 , Largo D. Dinis, 3000-143 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9307-097X","authenticated-orcid":false,"given":"Sa\u00efd","family":"Benayadi","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques IECL UMR CNRS 7502, Universit\u00e9 de Lorraine 2 , 3 Rue Augustin Fresnel, BP 45112, F-57073 Metz Cedex 03, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0363-6245","authenticated-orcid":false,"given":"Rosa M.","family":"Navarro","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Extremadura 3 , C\u00e1ceres, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4842-6735","authenticated-orcid":false,"given":"Jos\u00e9 M.","family":"S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Campus de Puerto Real, Universidad de C\u00e1diz 4 , 11510 Puerto Real, C\u00e1diz, Spain"}]}],"member":"317","published-online":{"date-parts":[[2023,4,13]]},"reference":[{"key":"2023081023492065500_c1","doi-asserted-by":"publisher","first-page":"724","DOI":"10.1016\/j.jpaa.2008.09.016","article-title":"Quadratic Lie superalgebras with a reductive even part","volume":"213","year":"2009","journal-title":"J. Pure Appl. Algebra"},{"key":"2023081023492065500_c2","doi-asserted-by":"publisher","first-page":"2400","DOI":"10.1063\/1.523598","article-title":"A classification of four-dimensional Lie superalgebras","volume":"19","year":"1978","journal-title":"J. Math. Phys."},{"key":"2023081023492065500_c3","unstructured":"Bajo, I., Benayadi, S., and Bordemann, M., \u201cGeneralized double extension and descriptions of quadratic Lie superalgebras,\u201d arXiv:math-ph\/0712.0228 (2007)."},{"key":"2023081023492065500_c4","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1016\/j.jalgebra.2007.06.001","article-title":"Symplectic structures on quadratic Lie algebras","volume":"316","year":"2007","journal-title":"J. Algebra"},{"key":"2023081023492065500_c5","doi-asserted-by":"publisher","first-page":"582","DOI":"10.1016\/j.jalgebra.2008.09.026","article-title":"Quadratic symplectic Lie superalgebras and Lie bi-superalgebras","volume":"321","year":"2009","journal-title":"J. Algebra"},{"key":"2023081023492065500_c6","first-page":"917","article-title":"On Lie superalgebras with a filiform module as an odd part","volume":"32","year":"2022","journal-title":"J. Lie Theory"},{"key":"2023081023492065500_c7","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1080\/00927879908826421","article-title":"Double extension of quadratic Lie superalgebras","volume":"27","year":"1999","journal-title":"Commun. Algebra"},{"key":"2023081023492065500_c8","doi-asserted-by":"publisher","first-page":"3867","DOI":"10.1080\/00927879508825437","article-title":"Structures de certaines alg\u00e8bres de Lie quadratiques","volume":"23","year":"1995","journal-title":"Commun. Algebra"},{"key":"2023081023492065500_c9","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1006\/jabr.1999.8067","article-title":"Quadratic Lie superalgebras with the completely reducible action of the even part on the odd part","volume":"223","year":"2000","journal-title":"J. Algebra"},{"key":"2023081023492065500_c10","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/j.jalgebra.2022.09.019","article-title":"Manin triples and non-degenerate anti-symmetric bilinear forms on Lie superalgebras in characteristic 2","volume":"614","year":"2023","journal-title":"J. Algebra"},{"key":"2023081023492065500_c11","first-page":"151","article-title":"Nondegenerate invariant bilinear forms on nonassociative algebras","volume":"66","year":"1997","journal-title":"Acta Math. Univ. Comenianae"},{"key":"2023081023492065500_c12","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1007\/s10468-018-9802-8","article-title":"Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras","volume":"21","year":"2018","journal-title":"Algebras Representation Theory"},{"key":"2023081023492065500_c13","article-title":"Double and Lagrangian extensions for quasi-Frobenius Lie superalgebras","journal-title":"J. Algebra its Appl. (to be published)"},{"key":"2023081023492065500_c14","first-page":"119","article-title":"A classification of solvable quadratic and odd quadratic Lie superalgebras in low dimensions","volume":"55","year":"2014","journal-title":"Rev. Union Mat. Argent."},{"key":"2023081023492065500_c15","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1016\/j.jalgebra.2014.02.034","article-title":"Singular quadratic Lie superalgebras","volume":"407","year":"2014","journal-title":"J. Algebra"},{"key":"2023081023492065500_c16","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/bf01077870","article-title":"Frobenius Lie algebras","volume":"16","year":"1982","journal-title":"Funct. Anal. Appl."},{"key":"2023081023492065500_c17","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1006\/jabr.1996.0237","article-title":"Lie superalgebras with semisimple even part","volume":"183","year":"1996","journal-title":"J. Algebra"},{"key":"2023081023492065500_c18","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/0021-8693(87)90209-2","article-title":"Symmetric, invariant, non-degenerate bilinear form on Lie algebra","volume":"105","year":"1987","journal-title":"J. Algebra"},{"key":"2023081023492065500_c19","doi-asserted-by":"publisher","first-page":"4121","DOI":"10.1063\/1.531620","article-title":"On the structure of symmetric self-dual Lie algebras","volume":"37","year":"1996","journal-title":"J. Math. Phys."},{"key":"2023081023492065500_c20","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1016\/j.geomphys.2004.01.003","article-title":"Some problems concerning to nilpotent Lie superalgebras","volume":"51","year":"2004","journal-title":"J. Geom. Phys."},{"key":"2023081023492065500_c21","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1017\/s0004972700002835","article-title":"Invariant quadratic forms on finite dimensional Lie algebras","volume":"33","year":"1986","journal-title":"Bull. Aust. Math. Soc."},{"key":"2023081023492065500_c22","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1090\/s0002-9939-1955-0068532-9","article-title":"A note on automorphisms and derivations of Lie algebras","volume":"6","year":"1955","journal-title":"Proc. Am. Math. Soc."},{"key":"2023081023492065500_c23","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s00031-005-1106-5","article-title":"Metric Lie algebras and quadratic extensions","volume":"11","year":"2006","journal-title":"Transform. Groups"},{"key":"2023081023492065500_c24","doi-asserted-by":"publisher","first-page":"553","DOI":"10.24033\/asens.1496","article-title":"Alg\u00e8bres de Lie et produit scalaire invariant","volume":"18","year":"1985","journal-title":"Ann. Sci. \u00c8c. Norm. Super."},{"key":"2023081023492065500_c25","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1080\/00927878008822445","article-title":"On Frobenius Lie algebras","volume":"8","year":"1980","journal-title":"Commun. Algebra"},{"key":"2023081023492065500_c26","doi-asserted-by":"publisher","first-page":"1650190","DOI":"10.1142\/s0219498816501905","article-title":"On indecomposable solvable Lie superalgebras having a Heisenberg nilradical","volume":"15","year":"2016","journal-title":"J. Algebra Appl."},{"key":"2023081023492065500_c27","volume-title":"The Theory of Lie Superalgebras","year":"1979"}],"container-title":["Journal of Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jmp\/article-pdf\/doi\/10.1063\/5.0142935\/16826059\/041703_1_5.0142935.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jmp\/article-pdf\/doi\/10.1063\/5.0142935\/16826059\/041703_1_5.0142935.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T23:49:32Z","timestamp":1691711372000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jmp\/article\/64\/4\/041703\/2878091\/Quadratic-symplectic-Lie-superalgebras-with-a"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,1]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,4,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0142935","relation":{},"ISSN":["0022-2488","1089-7658"],"issn-type":[{"value":"0022-2488","type":"print"},{"value":"1089-7658","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,4,1]]},"published":{"date-parts":[[2023,4,1]]},"article-number":"041703"}}