Finkel Morgenstern, FedericoGonzález López, ArtemioRodríguez González, Miguel Ángel2023-06-202023-06-201997-10-070305-447010.1088/0305-4470/30/19/024https://hdl.handle.net/20.500.14352/59716©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.engjournal articlehttp://dx.doi.org/10.1088/0305-4470/30/19/024http://iopscience.iop.orghttp://arxiv.org/pdf/physics/9702015v1.pdfopen access51-73Física-Modelos matemáticosFísica matemática