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

FU Hong-Chen

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《中国物理C》（英文）编辑部

2024年10月30日

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

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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).

[1]	K. I. Beloborodov , A. V. Berdyugin , A. A. Botov , V. B. Golubev , T. V. Dimova , V. P. Druzhinin , A. G. Kharlamov , D. P. Kovrizhin , I. A. Koop , A. A. Korol , S. V. Koshuba , A. E. Obrazovsky , E. V. Pakhtusova , D. A. Shtol , S. I. Serednyakov , Z. K. Silagadze , A. N. Skrinsky , Yu. A. Tikhonov , Yu. M. Shatunov , A. V. Vasil'ev . Study of the process e⁺e^－→π⁺π^－π⁰π⁰ at energies √s<1 GeV. Chinese Physics C, 2010, 34(6): 680-685. doi: 10.1088/1674-1137/34/6/012
[2]	Jamil Aslam . B→0⁺(1⁺)+ missing energy in unparticle physics. Chinese Physics C, 2009, 33(5): 332-339. doi: 10.1088/1674-1137/33/5/003
[3]	DAI Lian-Rong , FU Yao , LIU Zhong-Zuo , WANG Yin , TONG Lei , LI Chun-Ran . Structure of Ξ^*Ω_(0,1/2) Dibaryon. Chinese Physics C, 2006, 30(S2): 271-273.
[4]	Yu Zhaoxian , Liu Yehou . Inhomogeneous Inverse Differential Realizations of the SU(1,1) Group. Chinese Physics C, 1999, 23(6): 529-535.
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[6]	BES Collaboration . Measurement of the Branching Ratios of τ^±→π^±+nπ⁰+ν_τ(n=0,1,2) decays. Chinese Physics C, 1997, 21(3): 193-200.
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[9]	FU Hong-Chen , GE Mo-Lin . Cyclic Representations of Quantum (Super) Algebras At q^p=1. Chinese Physics C, 1993, 17(8): 700-709.
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[11]	YU Zu-Rong . Irreducible Representations of Quantum Lie Superalgebra SL_q(2/1). Chinese Physics C, 1992, 16(11): 1035-1042.
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[13]	CHEN Xue-Jun . EXPRESSIONS OF FERMION OPERATORS IN THE INTERACTING BOSON-FERMION MODELS. Chinese Physics C, 1990, 14(2): 160-163.
[14]	SUN Chang-Pu . ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS. Chinese Physics C, 1990, 14(9): 788-795.
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[19]	ZHU Pei-Yu , CAO Yu-Fang , WU You-Shi . THE SPIN (6) LIMIT OF INTERACTING BOSON-FERMION MODEL Ⅱ. Chinese Physics C, 1985, 9(2): 154-160.
[20]	ZHANG XI-ZHEN , LI CHU-HSIA , . INTERACTING BOSON-FERMION MODEL AND. Chinese Physics C, 1982, 6(3): 347-354.

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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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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 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.