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Quasi-exactly solvable Lie superalgebras of differential operators
1997
Journal of Physics A: Mathematical and General
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In this paper, we study Lie superalgebras of 2× 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 nontrivial, 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
doi:10.1088/0305-4470/30/19/024
fatcat:ycvy6nvj7vfdzcylhi5gbfvqfy