Abstract
We give a classification of Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras \(\mathfrak{sv}\). Then we find out that not all Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras \(\mathfrak{sv}\) are triangular coboundary.
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Chen H, Fan G, Han J, Su Y. Structures of generalized loop Schrödinger-Virasoro algebras. Mediterr J Math, 2018, 15: 125
Chen H, Han J, Su Y, Xu Y. Loop Schrödinger-Virasoro Lie conformal algebra. Internat J Math, 2016, 6: 1650057
Drinfeld V G. Constant quasiclassical solutions of the Yang-Baxter quantum equation. Sov Math Dokl, 1983, 28: 667–671
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
Etingof P, Kazhdan D. Quantization of Lie bialgebras I. Selecta Math (N S), 1996, 2: 1–41
Fa H, Li J, Zheng Y. Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras. J Math Phys, 2015, 56: 111706
Han J, Li J, Su Y. Lie bialgebra structures on the Schrödinger-Virasoro Lie algebra. J Math Phys, 2009, 50: 083504
Henkel M. Schrödinger invariance and strongly anisotropic critical systems. J Stat Phys, 1994, 75: 1023–1029
Li J, Su Y. Representations of the Schrödinger-Virasoro algebras. J Math Phys, 2008, 49: 053512
Liu D, Pei Y, Zhu L. Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra. J Algebra, 2012, 359: 35–48
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
Song G, Su Y. Lie bialgebras of generalized Witt type. Sci China Ser A, 2006, 49: 533–544
Song G, Su Y. Dual Lie bialgebras of Witt and Virasoro types. Sci China Math, 2013, 43: 1093–1102
Taft E J. Witt and Virasoro algebras as Lie bialgebras. J Pure Appl Algebra, 1993, 87: 301–312
Tan S, Zhang X. Automorphisms and Verma modules for generalized Schrödinger-Virasoro algebras. J Algebra, 2009, 322: 1379–1394
Wang W, Li J, Xin B. Central extensions and derivations of generalized Schrödinger-Virasoro algebra. Algebra Colloq, 2012, 19: 735–744
Weibel C A. An Introduction to Homological Algebra. Cambridge Stud Adv Math. Cambridge: Cambridge Univ Press, 1994
Wu H, Wang S, Yue X. Structures of generalized loop Virasoro algebras. Comm Algebra, 2014, 42: 1545–1558
Wu H, Wang S. Yue X. Lie bialgebras of generalized loop Virasoro algebras. Chin Ann Math Ser B, 2015, 36(3): 437–446
Wu Y, Song G, Su Y. Lie bialgebras of generalized Virasoro-like type. Acta Math Sin (Engl Ser), 2006, 22: 1915–1922
Yang H, Su Y. Lie super-bialgebra structures on generalized super-virasoro algebras. Acta Math Sci Ser B Engl Ed, 2010, 30: 225–239
Yue X, Su Y. Lie bialgebra structures on Lie algebras of generalized Weyl type. Comm Algebra, 2008, 36: 1537–1549
Zhang X, Tan S. Unitary representations for the Schrödinger-Virasoro Lie algebra. J Algebra Appl, 2013, 12: 1250132
Acknowledgements
The authors would like to thank the referees for many helpful comments and suggestions. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11801369, 11771279, 11801363, 11431010) and the Natural Science Foundation of Shanghai (Grant No. 16ZR1415000).
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Chen, H., Dai, X. & Yang, H. Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras. Front. Math. China 14, 239–260 (2019). https://doi.org/10.1007/s11464-019-0761-0
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DOI: https://doi.org/10.1007/s11464-019-0761-0