Quasi-exactly Solvable Lie Superalgebras of Differential Operators
Finkel, Federico ; González-López, Artemio ; Rodríguez, Miguel A.
arXiv, 9702015 / Harvested from arXiv
Text on arXiv
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.
Publié le : 1997-02-17
Classification:  Mathematical Physics,  High Energy Physics - Theory,  Quantum Physics 
@article{9702015,
     author = {Finkel, Federico and Gonz\'alez-L\'opez, Artemio and Rodr\'\i guez, Miguel A.},
     title = {Quasi-exactly Solvable Lie Superalgebras of Differential Operators},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9702015}
}

Finkel, Federico; González-López, Artemio; Rodríguez, Miguel A. Quasi-exactly Solvable Lie Superalgebras of Differential Operators. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9702015/