%0 Journal Article
%A Finkel Morgenstern, Federico
%A González López, Artemio
%A Rodríguez González, Miguel Ángel
%T Quasi-exactly solvable Lie superalgebras of differential operators
%D 1997
%@ 0305-4470
%U https://hdl.handle.net/20.500.14352/59716
%X 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.
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