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Quasi-exactly solvable Lie superalgebras of differential operators Finkel Morgenstern, Federico González López, Artemio Rodríguez González, Miguel Ángel 51-73 Física-Modelos matemáticos Física matemática ©1997 IOP Publishing Ltd. This work was supported in part by DGICYT grant PB95-0401. 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. DGICYT Depto. de Física Teórica Fac. de Ciencias Físicas TRUE pub 2023-06-20T20:09:46Z 2023-06-20T20:09:46Z 1997-10-07 journal article https://hdl.handle.net/20.500.14352/59716 0305-4470 10.1088/0305-4470/30/19/024 eng PB95-0401 open access application/pdf IOP Publishing LTD