Quasi-exactly solvable Lie superalgebras of differential operators
| dc.contributor.author | Finkel Morgenstern, Federico | |
| dc.contributor.author | González López, Artemio | |
| dc.contributor.author | Rodríguez González, Miguel Ángel | |
| dc.date.accessioned | 2023-06-20T20:09:46Z | |
| dc.date.available | 2023-06-20T20:09:46Z | |
| dc.date.issued | 1997-10-07 | |
| dc.description | ©1997 IOP Publishing Ltd. This work was supported in part by DGICYT grant PB95-0401. | |
| dc.description.abstract | In this paper, we study Lie superalgebras of 2 x 2 matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional superalgebras whose odd subspace is non-trivial, we find those admitting a finite-dimensional invariant module of smooth vector-valued functions, and classify all the resulting finite-dimensional modules. The latter Lie superalgebras and their modules are the building blocks in the construction of quasi-exactly solvable quantum mechanical models for spin-1/2 particles in one dimension. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/32710 | |
| dc.identifier.doi | 10.1088/0305-4470/30/19/024 | |
| dc.identifier.issn | 0305-4470 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1088/0305-4470/30/19/024 | |
| dc.identifier.relatedurl | http://iopscience.iop.org | |
| dc.identifier.relatedurl | http://arxiv.org/pdf/physics/9702015v1.pdf | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59716 | |
| dc.issue.number | 19 | |
| dc.journal.title | Journal of physics A-Mathematical and general | |
| dc.language.iso | eng | |
| dc.page.final | 6892 | |
| dc.page.initial | 6879 | |
| dc.publisher | IOP Publishing LTD | |
| dc.relation.projectID | PB95-0401 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Quasi-exactly solvable Lie superalgebras of differential operators | |
| dc.type | journal article | |
| dc.volume.number | 303 | |
| dcterms.references | [1] Brihaye Y and Kosinski P 1994 Quasi exactly solvable 2 x 2 matrix quations J. Math. Phys. 35 3089–98 [2] Cotton É 1900 Sur les invariants différentiels de quelques équations aux dérivées partielles du second ordre Ann. E´cole Normale 17 211–44 [3] Finkel F, González-López A and Rodr´ıguez M A Quasi-exactly solvable spin 1=2 Schr¨odinger operators J. Math. Phys. in press [4] Finkel F and Kamran N On the equivalence of matrix valued differential operators to Schrödinger form J. Nonlin. Math. Phys. in press [5] Finkel F and Kamran N 1996 The Lie algebraic structure of differential operators admitting invariant spaces of polynomials Preprint q-alg/9612027 [6] González-López A, Kamran N and Olver P J 1991 Quasi-exactly solvable Lie algebras of first order differential operators in two complex variables J. Phys. A: Math. Gen. 24 3995–4008 [7] González-López A, Hurtubise J, Kamran N and Olver P J 1993 Quantification de la cohomologie des algèbres de Lie de champs de vecteurs et fibr´es en droites sur des surfaces complexes compactes C.R. Acad. Sci. (Paris) 316 1307–12 [8] González-López A, Kamran N and Olver P J 1996 Real Lie algebras of differential operators and quasi-exactly solvable potentials Phil. Trans. R. Soc. Lond. A 354 1165–93 [9] Kamran N and Olver P J 1990 Lie algebras of differential operators and Lie-algebraic potentials J. Math. Anal. Appl. 145 342–56 [10] Lie S 1880 Theorie der Transformationsgruppen Math. Ann. 16 441–528 | |
| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication | d781a665-7ef6-44e0-a0da-81f722f1b8ad | |
| relation.isAuthorOfPublication.latestForDiscovery | 207092a4-0443-4336-a037-15936f8acc25 |
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