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Representation theory of superconformal quantum mechanics. (English) Zbl 0654.17013
The superalgebra su(1,1/1) is the usual su(1,1)-Lie algebra augmented by two sets of spinorial operators Q,Q \(+\) and S,S \(+\) such that \(\{\) Q,Q \(+\}\) and \(\{\) S,S \(+\}\) are in su(1,1). Similarly su(2,2/1) is the augmented su(2,2) with spinorial generators. Some representations of these superalgebras and their possible use as spectrum generating algebras of some physical systems are discussed.
Reviewer: A.O.Barut

MSC:
17B70 Graded Lie (super)algebras
81Q99 General mathematical topics and methods in quantum theory
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17A70 Superalgebras
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References:
[1] DOI: 10.1016/0550-3213(81)90006-7 · Zbl 1258.81046
[2] DOI: 10.1016/0031-9163(65)90279-9
[3] DOI: 10.1016/0031-9163(65)90279-9
[4] DOI: 10.1016/0031-9163(65)90279-9
[5] DOI: 10.1016/0003-4916(80)90295-X
[6] DOI: 10.1016/0003-4916(80)90295-X
[7] DOI: 10.1016/0370-2693(84)91108-0
[8] DOI: 10.1016/0370-2693(84)91108-0
[9] DOI: 10.1088/0305-4470/20/5/024 · Zbl 0634.35074
[10] DOI: 10.1088/0305-4470/20/5/024 · Zbl 0634.35074
[11] DOI: 10.1007/BF01213405 · Zbl 1223.81094
[12] DOI: 10.1103/PhysRevD.32.2627
[13] DOI: 10.1063/1.1665653
[14] DOI: 10.1063/1.1665653
[15] DOI: 10.1063/1.523148 · Zbl 0354.17004
[16] DOI: 10.2307/1969129 · Zbl 0045.38801
[17] DOI: 10.1063/1.527193 · Zbl 0588.17005
[18] DOI: 10.1063/1.527193 · Zbl 0588.17005
[19] DOI: 10.1063/1.527193 · Zbl 0588.17005
[20] DOI: 10.1016/0370-1573(85)90023-7
[21] DOI: 10.1007/BF00406399 · Zbl 0552.17002
[22] DOI: 10.1007/BF00406399 · Zbl 0552.17002
[23] DOI: 10.1007/BF00406399 · Zbl 0552.17002
[24] DOI: 10.1007/BF00406399 · Zbl 0552.17002
[25] DOI: 10.1007/BF00406399 · Zbl 0552.17002
[26] DOI: 10.1063/1.1664804 · Zbl 0183.29003
[27] DOI: 10.1063/1.1664804 · Zbl 0183.29003
[28] DOI: 10.1063/1.1665078
[29] DOI: 10.1103/PhysRevD.32.2828
[30] DOI: 10.1103/PhysRevLett.57.1203
[31] DOI: 10.1088/0305-4616/9/11/006
[32] DOI: 10.1088/0305-4616/9/11/006
[33] DOI: 10.1016/0003-4916(74)90046-3
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