Publication: Quasi-exactly solvable Lie superalgebras of differential operators
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1997-10-07
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IOP Publishing LTD
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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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©1997 IOP Publishing Ltd.
This work was supported in part by DGICYT grant PB95-0401.
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