INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS

FU Hong-Chen

Chinese Physics C> 1990, Vol. 14> Issue(2) : 126-135

INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS

FU Hong-Chen ^,

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,and the corresponding inhomogeneous Boson-Fermion realization are studiel.A new kind of indecomposable and irreducible representations of Lie superalgebra B(0,1) is studied on the universal enveloping algebra of Heisenberg-Weyl superalgebra,and on its subspaces and quotient spaces.All the finite dimensional irreducible representations are naturally obtained as special cases.

References

[1]

A.V.Turbines and .A. G. Ushveridze; Phys. Lett., 126A(1987),181[2] A.V.Turbiner; Commun.Math Phys., 118(1988), 467-474.[3] M.A.Shifman; Preprint, CERN-TH. 5265/88, "New Findings in Quantum Mechanics".[4] Hong-Chen Fu and Chang-Pu Sun; Inhosnogeneous Boson Realization of Indecomposable Representations of Lie Algebras, J. Math. Phys., in press[5] Chang-Pu Sun; J. Phys. A: Math. Gen., 20(1987), 5823-5829.[6] P. A. M. Dirac; Int: J. Theor. Phys., 23(8)(1984), 677.[7] N. Jacobson; 'Basic Algebra.. Acdamic Press,1971.[8] 孙洪洲、韩其智，物理学进展,Vol. 3,No.1(1983).

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FU Hong-Chen. INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS[J]. Chinese Physics C, 1990, 14(2): 126-135.

FU Hong-Chen. INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS[J]. Chinese Physics C, 1990, 14(2): 126-135. shu

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Received: 1900-01-01
Revised: 1900-01-01

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INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS

FU Hong-Chen ^,

Corresponding author: FU Hong-Chen,

Department of Physics,Northeast Normal University,Changchun

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1990-02-05

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