Classification of minimal algebras over any field up to dimension 6.
| dc.contributor.author | Bazzoni, Giovanni | |
| dc.contributor.author | Muñoz, Vicente | |
| dc.date.accessioned | 2023-06-20T00:18:41Z | |
| dc.date.available | 2023-06-20T00:18:41Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | We give a classification of minimal algebras generated in degree 1, defined over any field k of characteristic different from 2, up to dimension 6. This recovers the classification of nilpotent Lie algebras over k up to dimension 6. In the case of a field k of characteristic zero, we obtain the classification of nilmanifolds of dimension less than or equal to 6, up to k-homotopy type. Finally, we determine which rational homotopy types of such nilmanifolds carry a symplectic structure. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MICINN | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16956 | |
| dc.identifier.doi | 10.1090/S0002-9947-2011-05471-1 | |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.officialurl | http://www.ams.org/journals/tran/2012-364-02/S0002-9947-2011-05471-1/S0002-9947-2011-05471-1.pdf | |
| dc.identifier.relatedurl | http://www.ams.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42375 | |
| dc.issue.number | 2 | |
| dc.journal.title | Transactions of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 1028 | |
| dc.page.initial | 1007 | |
| dc.publisher | American Mathematical Society | |
| dc.relation.projectID | MTM2007-63582. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 5151.1 | |
| dc.subject.keyword | Nilmanifolds | |
| dc.subject.keyword | rational homotopy | |
| dc.subject.keyword | Nilpotent Lie algebras | |
| dc.subject.keyword | Minimal model | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Classification of minimal algebras over any field up to dimension 6. | |
| dc.type | journal article | |
| dc.volume.number | 364 | |
| dcterms.references | Cerezo, A., Les algebres de Lie nilpotentes reelles et complexes de dimension 6, Prepublication J. Dieudonne,Univ. de Nice 27, 1983. Deligne, P., Griffiths P., Morgan J. and Sullivan D., Real Homotopy Theory of K¨ahler Manifolds,Inventiones Mathematicæ Vol. 29, 1975, p. 245-274. MR0382702 (52:3584) Felix, Y., Halperin, S. and Thomas, J.C., Rational Homotopy Theory, Graduate Texts in Mathematics 205, Springer, 2001. MR1802847 (2002d:55014) Goze, M. and Khakimdjanov, Y., Nilpotent Lie algebras, Mathematics and Its Applications 361, Kluwer, 1996.MR1383588 (97e:17017) de Graaf, W. A. Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, Journal of Algebra 309, 2007, 640-653. MR2303198 (2007k:17012) Griffiths, P. and Morgan, J. Rational Homotopy Theory and Differential Forms, Progress in Mathematics,Birkh¨auser, 1981. MR641551 (82m:55014) Halperin, S. Universal enveloping algebras and loop space homology, Journal of Pure and Applied Algebra 83, 1992, 237-282. MR1194839 (93k:55014) Lehmann, D., Sur la generalisation d` un theoreme de Tischler a certains feuilletages nilpotents, Nederl. Akad. Wetensch. Indag. Math. 41, 1979, 177-189. MR535566 (80f:57013) Lupton, G., The Rational Toomer Invariant and Certain Elliptic Spaces, Contemporary Mathematics 316, 2004, 135-146. MR1962160 (2004a:55009) Magnin, L., Sur les algebres de Lie nilpotentes de dimension ≤ 7, Journal of Geometry and Physics 3, 1986, 119-144. MR855573 (87k:17012) Morgan, J., The Algebraic Topology of Smooth Algebraic Varieties, Publications Mathematiques de l’I.H.E.S 48, 1978, 137-204. MR516917 (80e:55020) Nomizu, K., On the cohomology of compact homogeneous spaces of nilpotent Lie groups,Annals of Mathematics (2) 59, 1954, 531-538. MR0064057 (16:219c) Oprea, J. and Tralle, A., Symplectic Manifolds with no Kähler Structure, Lecture Notes in Mathematics 1661,Springer, 1997. MR1465676 (98k:53038) Salamon, S. Complex structures on nilpotent Lie algebras, Journal of Pure and Applied Algebra 157, 2001, 311-333. MR1812058 (2002g:53089) Sullivan, D., Infinitesimal Computations in Topology,Publications Math´ematiques de l’I.H.E.S. 47,1997, 269-331. MR0646078 (58:31119) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | a4ff6e44-3e75-4543-9b26-ef3df104750a | |
| relation.isAuthorOfPublication.latestForDiscovery | a4ff6e44-3e75-4543-9b26-ef3df104750a |
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