Chinese Physics C > 1990, Vol. 14 > Issue(S1): 27-37

Inhomogeneous Differential Realization, Boson-Fermion Realization of Lie SuperalgebraB(0,1) and its Representations

Fu Hongchen

Department of Physics, Northeast Normal University, Changchun

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Abstract：
The differential realization of Lie superalgebra B(0,1) on the space of inhomogeneous polynomials (called inhomogeneous differential realization), and the corresponding inhomogeneous Boson-Fermion realization are studied. By making use of the inhomogeneous Boson-Fermion realization, a new kind of indecomposable and irreducible representation of Lie superalgebra B(0,1) is studied on the universal enveloping algebra of Heisenberg-Weyl superalgebra, its subspaces and its quotient spaces; AH the finite dimensional irreducible representations of Lie superalgebra B(0,1) are naturally obtained as special cases.

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Fu Hongchen. Inhomogeneous Differential Realization, Boson-Fermion Realization of Lie Superalgebra B(0,1) and its Representations[J]. Chinese Physics C, 1990, 14(S1): 27-37.

Fu Hongchen. Inhomogeneous Differential Realization, Boson-Fermion Realization of Lie Superalgebra B(0,1) and its Representations[J]. Chinese Physics C, 1990, 14(S1): 27-37. shu

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Received: 1989-04-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Inhomogeneous Differential Realization, Boson-Fermion Realization of Lie SuperalgebraB(0,1) and its Representations

Fu Hongchen

Department of Physics, Northeast Normal University, Changchun

Received Date:1989-04-01

Abstract:The differential realization of Lie superalgebraB(0,1) on the space of inhomogeneous polynomials (called inhomogeneous differential realization), and the corresponding inhomogeneous Boson-Fermion realization are studied. By making use of the inhomogeneous Boson-Fermion realization, a new kind of indecomposable and irreducible representation of Lie superalgebraB(0,1) is studied on the universal enveloping algebra of Heisenberg-Weyl superalgebra, its subspaces and its quotient spaces; AH the finite dimensional irreducible representations of Lie superalgebraB(0,1) are naturally obtained as special cases.