dorsal/arxiv
View SchemaQuasi-exactly Solvable Lie Superalgebras of Differential Operators
| Authors | Federico Finkel, Artemio González-López, Miguel A. Rodríguez |
|---|---|
| Categories | |
| ArXiv ID | physics/9702015 |
| URL | https://arxiv.org/abs/physics/9702015 |
| DOI | 10.1088/0305-4470/30/19/024 |
| Journal | J.Phys.A30:6879-6892,1997 |
Abstract
In this paper, we study Lie superalgebras of $2\times 2$ 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 nontrivial, 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 QES quantum mechanical models for spin 1/2 particles in one dimension.
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"abstract": "In this paper, we study Lie superalgebras of $2\\times 2$ matrix-valued\nfirst-order differential operators on the complex line. We first completely\nclassify all such superalgebras of finite dimension. Among the\nfinite-dimensional superalgebras whose odd subspace is nontrivial, we find\nthose admitting a finite-dimensional invariant module of smooth vector-valued\nfunctions, and classify all the resulting finite-dimensional modules. The\nlatter Lie superalgebras and their modules are the building blocks in the\nconstruction of QES quantum mechanical models for spin 1/2 particles in one\ndimension.",
"arxiv_id": "physics/9702015",
"authors": [
"Federico Finkel",
"Artemio Gonz\u00e1lez-L\u00f3pez",
"Miguel A. Rodr\u00edguez"
],
"categories": [
"math-ph",
"hep-th",
"math.MP",
"quant-ph"
],
"doi": "10.1088/0305-4470/30/19/024",
"journal_ref": "J.Phys.A30:6879-6892,1997",
"title": "Quasi-exactly Solvable Lie Superalgebras of Differential Operators",
"url": "https://arxiv.org/abs/physics/9702015"
},
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