Classification of Lie algebras with naturally graded quasi-filiform nilradicals
| dc.contributor.author | Ancochea Bermúdez, José María | |
| dc.contributor.author | Campoamor Stursberg, Otto-Rudwig | |
| dc.contributor.author | García Vergnolle, Lucía | |
| dc.date.accessioned | 2023-06-20T03:31:49Z | |
| dc.date.available | 2023-06-20T03:31:49Z | |
| dc.date.issued | 2011 | |
| dc.description.abstract | The whole class of complex Lie algebras g having a naturally graded nilradical with characteristic sequence c(g) = (dim g − 2, 1, 1) is classified. It is shown that up to one exception, such Lie algebras are solvable. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MEC | |
| dc.description.sponsorship | UCM-BSCH | |
| dc.description.sponsorship | Fundación Ramon Areces | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20685 | |
| dc.identifier.doi | 10.1016/j.geomphys.2011.06.015 | |
| dc.identifier.issn | 0393-0440 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0393044011001604 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/43734 | |
| dc.issue.number | 11 | |
| dc.journal.title | Journal of Geometry and Physics | |
| dc.language.iso | eng | |
| dc.page.final | 2186 | |
| dc.page.initial | 2168 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | MTM2006-09152 | |
| dc.relation.projectID | GR58/4120818-920920 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.81 | |
| dc.subject.keyword | Solvable | |
| dc.subject.keyword | Lie algebras | |
| dc.subject.keyword | Extensions | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | Classification of Lie algebras with naturally graded quasi-filiform nilradicals | |
| dc.type | journal article | |
| dc.volume.number | 61 | |
| dcterms.references | J.M. Ancochea, M. Goze, Sur la classification des algèbres de Lie nilpotentes de dimension 7, C. R. Acad. Sci. 302 (1986) 611–613. R. Campoamor-Stursberg, Razreshimye algebry Li, zadannye proizvedeniem obrazuyushchikh i nekotorye ikh prilozheniya, Fundam. Prikl. Mat. 11 (2005) 85–94. M. Goto, Note on a characterization of solvable Lie algebras, J. Sci. Hiroshima Univ. Ser. A–I 26 (1962) 1–2. V.V. Morozov, Klassifikaciya nil’potentnykh algebr Lie shestovo poryadka, Izv. Vyssh. Uchebn. Zaved. Mat. 4 (1958) 161–171. G.M. Mubarakzyanov, Klassifikaciya razreshimykh algebr Lie shestovo poryadka s odnim nenilpotentym bazisnym elementom, Izv. Vyssh. Uchebn. Zaved. Mat. 35 (1963) 104–116. È.N. Safiullina, Voprosu o klassifikacii nil’potentnykh algebr Li sed’mogo poryadka, VINITI, 1976, pp. 1702–1776. P. Turkowski, Solvable Lie algebras of dimension six, J. Math. Phys. 31 (1990) 1344–1350. J. Patera, H. Zassenhaus, On Lie gradings. I, Linear Algebra Appl. 112 (1989) 87–159. M. Havlícek, J. Patera, E. Pelantova, On Lie gradings. II, Linear Algebra Appl. 277 (1998) 97–125. A. Nijenhuis, R.W. Richardson, Deformations of Lie algebra structures, J. Math. Mech. 17 (1967) 89–105. M. Vergne, Cohomologies des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes, Bull. Soc. Math. France 98 (1970) 81–116. J.M. Ancochea, R. Campoamor-Stursberg, L. García Vergnolle, Solvable Lie algebras with naturally graded nilradicals and their invariants, J. Phys. A 39 (2006) 1339–1355. L. Šnobl, P. Winternitz, A class of solvable Lie algebras and their Casimir invariants, J. Phys. A 38 (2005) 2687–2700. J.R. Gómez, A. Jiménez-Merchán, Naturally graded quasi-filiform Lie algebras, J. Algebra 256 (2002) 221–228. L. García Vergnolle, Sur les algèbres de Lie quasi-iliformes admettant un tore de dérivations, Manuscripta Math. 124 (2007) 489–505. Y. Wang, J. Lin, S. Deng, Solvable Lie algebras with quasifiliform nilradicals, Comm. Algebra 36 (2008) 4052–4067. A.I. Mal’cev, Solvable Lie algebras, Izv. Akad. Nauk SSSR 9 (1945) 329–356. G.B. Mubarakzyanov, Nekotorye teoremy o razreshimykh algebrakh Li, Izv. Vyssh. Uchebn. Zaved. Mat. 55 (1966) 95–98. R. Campoamor-Stursberg, Some remarks concerning the invariants of rank one solvablereal Lie algebras, Algebra Colloq. 12 (2005) 497–518. A. Ballesteros, F.J. Herranz, A. Blasco, (Super) integrability from coalgebra symmetry: formalism and applications, J. Phys. Conf. Ser. 175 (2009) 012004 (16 pp). | |
| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication | 72801982-9f3c-4db0-b765-6e7b4aa2221b | |
| relation.isAuthorOfPublication.latestForDiscovery | 8afd7745-e428-4a77-b1ff-813045b673fd |
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