Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras

Haibo CHEN , Xiansheng DAI , Hengyun YANG

Front. Math. China ›› 2019, Vol. 14 ›› Issue (2) : 239 -260.

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Front. Math. China ›› 2019, Vol. 14 ›› Issue (2) : 239 -260. DOI: 10.1007/s11464-019-0761-0
RESEARCH ARTICLE
RESEARCH ARTICLE

Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras

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Abstract

We give a classification of Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras sv. Then we find out that not all Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras sv are triangular coboundary.

Keywords

Lie bialgebra / Yang-Baxter equation / generalized loop Schrödinger-Virasoro algebra

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Haibo CHEN, Xiansheng DAI, Hengyun YANG. Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras. Front. Math. China, 2019, 14(2): 239-260 DOI:10.1007/s11464-019-0761-0

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References

[1]

Chen H, Fan G, Han J, Su Y. Structures of generalized loop Schrödinger-Virasoro algebras. Mediterr J Math, 2018, 15: 125

[2]

Chen H, Han J, Su Y, Xu Y. Loop Schrödinger-Virasoro Lie conformal algebra. Internat J Math, 2016, 6: 1650057

[3]

Drinfeld V G. Constant quasiclassical solutions of the Yang-Baxter quantum equation. Sov Math Dokl, 1983, 28: 667–671

[4]

Drinfeld V G. Quantum groups. In: Proceedings of the International Congress of Mathematicians, 1986, Berkeley, California, USA, Vol 1. Providence: Amer Math Soc, 1987, 798–820

[5]

Etingof P, Kazhdan D. Quantization of Lie bialgebras I. Selecta Math (N S), 1996, 2: 1–41

[6]

Fa H, Li J, Zheng Y. Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras. J Math Phys, 2015, 56: 111706

[7]

Han J, Li J, Su Y. Lie bialgebra structures on the Schrödinger-Virasoro Lie algebra. J Math Phys, 2009, 50: 083504

[8]

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

[9]

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

[10]

Liu D, Pei Y, Zhu L. Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra. J Algebra, 2012, 359: 35–48

[11]

Ng S H, Taft E J. Classification of the Lie bialgebra structures on the Witt and Virasoro algebras. J Pure Appl Algebra, 2000, 151: 67–88

[12]

Song G, Su Y. Lie bialgebras of generalized Witt type. Sci China Ser A, 2006, 49: 533–544

[13]

Song G, Su Y. Dual Lie bialgebras of Witt and Virasoro types. Sci China Math, 2013, 43: 1093–1102

[14]

Taft E J. Witt and Virasoro algebras as Lie bialgebras. J Pure Appl Algebra, 1993, 87: 301–312

[15]

Tan S, Zhang X. Automorphisms and Verma modules for generalized Schrödinger-Virasoro algebras. J Algebra, 2009, 322: 1379–1394

[16]

Wang W, Li J, Xin B. Central extensions and derivations of generalized Schrödinger-Virasoro algebra. Algebra Colloq, 2012, 19: 735–744

[17]

Weibel C A. An Introduction to Homological Algebra. Cambridge Stud Adv Math. Cambridge: Cambridge Univ Press, 1994

[18]

Wu H, Wang S, Yue X. Structures of generalized loop Virasoro algebras. Comm Algebra, 2014, 42: 1545–1558

[19]

Wu H, Wang S. Yue X. Lie bialgebras of generalized loop Virasoro algebras. Chin Ann Math Ser B, 2015, 36(3): 437–446

[20]

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

[21]

Yang H, Su Y. Lie super-bialgebra structures on generalized super-virasoro algebras. Acta Math Sci Ser B Engl Ed, 2010, 30: 225–239

[22]

Yue X, Su Y. Lie bialgebra structures on Lie algebras of generalized Weyl type. Comm Algebra, 2008, 36: 1537–1549

[23]

Zhang X, Tan S. Unitary representations for the Schrödinger-Virasoro Lie algebra. J Algebra Appl, 2013, 12: 1250132

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