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Quasi-exactly solvable Lie superalgebras of differential operators

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Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel (1997) Quasi-exactly solvable Lie superalgebras of differential operators. Journal of physics A-Mathematical and general, 303 (19). pp. 6879-6892. ISSN 0305-4470

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Official URL: http://dx.doi.org/10.1088/0305-4470/30/19/024




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.


Item Type:Article
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©1997 IOP Publishing Ltd.
This work was supported in part by DGICYT grant PB95-0401.

Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32710
Deposited On:30 Jul 2015 09:02
Last Modified:10 Dec 2018 15:10

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