Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras

Abstract

We give a classification of Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras \mathfrak{s}\mathfrak{v}. 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

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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