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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Abstract
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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[1] Brihaye Y and Kosinski P 1994 Quasi exactly solvable 2 x 2 matrix quations J. Math. Phys. 35 3089–98
[2] Cotton É 1900 Sur les invariants différentiels de quelques équations aux dérivées partielles du second ordre Ann. E´cole Normale 17 211–44
[3] Finkel F, González-López A and Rodr´ıguez M A Quasi-exactly solvable spin 1=2 Schr¨odinger operators J. Math. Phys. in press
[4] Finkel F and Kamran N On the equivalence of matrix valued differential operators to Schrödinger form J. Nonlin. Math. Phys. in press
[5] Finkel F and Kamran N 1996 The Lie algebraic structure of differential operators admitting invariant spaces of polynomials Preprint q-alg/9612027
[6] González-López A, Kamran N and Olver P J 1991 Quasi-exactly solvable Lie algebras of first order differential operators in two complex variables J. Phys. A: Math. Gen. 24 3995–4008
[7] González-López A, Hurtubise J, Kamran N and Olver P J 1993 Quantification de la cohomologie des algèbres de Lie de champs de vecteurs et fibr´es en droites sur des surfaces complexes compactes C.R. Acad. Sci. (Paris) 316 1307–12
[8] González-López A, Kamran N and Olver P J 1996 Real Lie algebras of differential operators and quasi-exactly solvable potentials Phil. Trans. R. Soc. Lond. A 354 1165–93
[9] Kamran N and Olver P J 1990 Lie algebras of differential operators and Lie-algebraic potentials J. Math. Anal. Appl. 145 342–56
[10] Lie S 1880 Theorie der Transformationsgruppen Math. Ann. 16 441–528