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A supertrace identity and its applications to superintegrable systems. (English) Zbl 1153.81398
Summary: A supertrace identity on Lie superalgebras is established. It provides a tool for constructing super-Hamiltonian structures of zero curvature equations associated with Lie superalgebras. Applications in the case of the Lie superalgebra \(B(0,1)\) present super-Hamiltonian structures of a super-AKNS soliton hierarchy and a super-Dirac soliton hierarchy.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
17B80 Applications of Lie algebras and superalgebras to integrable systems
81R12 Groups and algebras in quantum theory and relations with integrable systems
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References:
[1] DOI: 10.1063/1.528449 · Zbl 0678.70015 · doi:10.1063/1.528449
[2] DOI: 10.1088/0305-4470/22/13/031 · Zbl 0697.58025 · doi:10.1088/0305-4470/22/13/031
[3] DOI: 10.1088/0305-4470/39/34/013 · Zbl 1104.70011 · doi:10.1088/0305-4470/39/34/013
[4] DOI: 10.1007/BF00397758 · Zbl 0585.58020 · doi:10.1007/BF00397758
[5] DOI: 10.1007/BF02104982 · Zbl 0556.58014 · doi:10.1007/BF02104982
[6] DOI: 10.1007/978-94-009-3799-4 · doi:10.1007/978-94-009-3799-4
[7] DOI: 10.1007/BF00398956 · Zbl 0667.58013 · doi:10.1007/BF00398956
[8] DOI: 10.1007/BF01790347 · Zbl 0699.58036 · doi:10.1007/BF01790347
[9] Ma W. X., Chin. Ann. Math., Ser. A 13 pp 115– (1992)
[10] DOI: 10.1088/0305-4470/26/11/009 · Zbl 0789.35144 · doi:10.1088/0305-4470/26/11/009
[11] DOI: 10.1016/0375-9601(93)91135-R · doi:10.1016/0375-9601(93)91135-R
[12] DOI: 10.1007/BF01211044 · Zbl 0607.35075 · doi:10.1007/BF01211044
[13] DOI: 10.1016/S0370-2693(99)00041-6 · Zbl 0966.37033 · doi:10.1016/S0370-2693(99)00041-6
[14] DOI: 10.1063/1.523777 · Zbl 0383.35065 · doi:10.1063/1.523777
[15] Tu G. Z., Sci. Sin., Ser. A 29 pp 138– (1986)
[16] DOI: 10.1088/0305-4470/38/40/005 · Zbl 1077.37045 · doi:10.1088/0305-4470/38/40/005
[17] Scheunert M., The Theory of Superalgebras (1978) · Zbl 0407.17001
[18] Sun H. Z., Lie Algebras and Lie Superalgebras and Their Applications in Physics (1999)
[19] DOI: 10.1016/0375-9601(85)90033-7 · doi:10.1016/0375-9601(85)90033-7
[20] DOI: 10.1002/sapm1974534249 · Zbl 0408.35068 · doi:10.1002/sapm1974534249
[21] DOI: 10.1063/1.527309 · Zbl 0614.70014 · doi:10.1063/1.527309
[22] DOI: 10.1063/1.528881 · Zbl 0705.58024 · doi:10.1063/1.528881
[23] DOI: 10.1088/0266-5611/12/6/001 · Zbl 0861.35091 · doi:10.1088/0266-5611/12/6/001
[24] Ma W. X., Chin. Ann. Math., Ser. B 18 pp 79– (1997)
[25] DOI: 10.1088/0305-4470/30/2/023 · Zbl 0947.37039 · doi:10.1088/0305-4470/30/2/023
[26] DOI: 10.1063/1.1388898 · Zbl 1063.37065 · doi:10.1063/1.1388898
[27] DOI: 10.1142/S0252959902000341 · Zbl 1183.37109 · doi:10.1142/S0252959902000341
[28] DOI: 10.1016/j.physleta.2005.09.089 · Zbl 1181.37101 · doi:10.1016/j.physleta.2005.09.089
[29] DOI: 10.1063/1.528090 · Zbl 0665.35076 · doi:10.1063/1.528090
[30] DOI: 10.1007/BF02108075 · Zbl 0790.35097 · doi:10.1007/BF02108075
[31] DOI: 10.1007/BF02099553 · Zbl 0852.35127 · doi:10.1007/BF02099553
[32] DOI: 10.1142/S0217732397002752 · Zbl 0908.58087 · doi:10.1142/S0217732397002752
[33] DOI: 10.1007/1-4020-3088-6 · doi:10.1007/1-4020-3088-6
[34] DOI: 10.1088/0305-4470/38/5/008 · Zbl 1062.37089 · doi:10.1088/0305-4470/38/5/008
[35] DOI: 10.1016/0375-9601(94)90616-5 · doi:10.1016/0375-9601(94)90616-5
[36] DOI: 10.2991/jnmp.2002.9.s1.10 · Zbl 1362.35026 · doi:10.2991/jnmp.2002.9.s1.10
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