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2-Cocycles of original deformative Schrödinger-Virasoro algebras

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Abstract

Both original and twisted Schrödinger-Virasoro algebras, and also their deformations were introduced and investigated in a series of papers by Henkel, Roger and Unterberger. In the present paper we aim at determining the 2-cocycles of original deformative Schrödinger-Virasoro algebras.

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References

  1. Henkel M. Schrödinger invariance and strongly anisotropic critical systems. J Stat Phys, 75: 1023–1029 (1994)

    Article  MATH  Google Scholar 

  2. Henkel M, Unterberger J. Schrödinger invariance and space-time symmetries. Nuclear Phys B, 660: 407–412 (2003)

    MATH  MathSciNet  Google Scholar 

  3. Roger C, Unterberger J. The Schrödinger-Virasoro Lie group and algebra: representation theory and cohomological study. Ann Henri Poincaré, 7: 1477–1529 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Unterberger J. On vertex algebra representations of the Schrödinger-Virasoro algebra. arXiv:cond-mat/0703 214v2 (2007)

  5. Li J, Su Y. The derivation algebra and automorphism group of the twisted Schrödinger-Virasoro algebra. arXiv: 0801.2207v1 (2008)

  6. Gao S, Jiang C, Pei Y. Structure of the extended Schrödinger-Virasoro Lie algebra. Algebra Colloq (in press)

  7. Li J, Su Y. Representations of the Schrödinger-Virasoro algebras. J Math Phys, 49(5): 053512 (2008)

    Article  MathSciNet  Google Scholar 

  8. Li J, Su Y. 2-cocycles of twisted deformative Schrödinger-Virasoro algebras. arXiv: 0801.2210v1 (2008)

  9. Su Y. Derivations of generalized Weyl algebras. Sci China Ser A-Math, 46: 346–354 (2003)

    Google Scholar 

  10. Xin B, Song G, Su Y. Hamiltonian type Lie bialgebras. Sci China Ser A-Math, 50: 1267–1279 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Song G, Su Y. Lie bialgebras of generalized Witt type. Sci China Ser A-Math, 49(1): 1–12 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Wu Y, Song G, Su Y. Lie bialgebras of generalized Virasoro-like type, Acta Math Sin-Engl Ser, 22(6): 1915–1922 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Bakalov B, Kac V G, Voronov A A. Cohomology of conformal algebras. Comm Math Phys, 200: 561–598 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Scheunert M, Zhang R B. Cohomology of Lie superalgebras and their generalizations. J Math Phys, 39: 5024–5061 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chen H, Gao Y, Shang S. B(0, N)-graded Lie superalgebras coordinatized by quantum tori. Sci China Ser A-Math, 49(11): 1740–1752 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Su Y. 2-cocycles on the Lie algebras of all differential operators of several indeterminates (in Chinese). Northeastern Math J, 6: 365–368 (1990)

    MATH  Google Scholar 

  17. Su Y. 2-cocycles on the Lie algebras of generalized differential operators. Comm Algebra, 30: 763–782 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  18. Su Y. Low dimensional cohomology of general conformal algebras gc N. J Math Phys, 45: 509–524 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Su Y, Zhao K. Second cohomology group of generalized Witt type Lie algebras and certain reperesentations. Comm Algebra, 30: 3285–3309 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to JunBo Li.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471091, 10671027), Foundation of Shanghai Education Committee (Grant No. 06FZ029) and “One Hundred Talents Program” from University of Science and Technology of China

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Li, J., Su, Y. & Zhu, L. 2-Cocycles of original deformative Schrödinger-Virasoro algebras. Sci. China Ser. A-Math. 51, 1989–1999 (2008). https://doi.org/10.1007/s11425-008-0115-y

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  • DOI: https://doi.org/10.1007/s11425-008-0115-y

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