Abstract
In this paper we obtain that every super-Virasoro algebra admits only triangular coboundary Lie super-bialgebra structures and this is proved mainly based on the computation of derivations from the super-Virasoro algebra to the tensor product of its adjoint module.
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References
Drinfeld V G. Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang-Baxter equations. Dokl Akad Nauk SSSR, 1983, 268: 285–287 (Russian)
Drinfeld V G. Quantum groups. In: Proceeding of the International Congress of Mathematicians, Vol 1, 2, Berkeley, Calif, 1986. Providence: Amer Math Soc, 1987, 798–820
Michaelis W. A class of infinite-dimensional Lie bialgebras containing the Virasoro algebras. Adv Math, 1994, 107: 365–392
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
Nichols W D. The structure of the dual Lie coalgebra of the Witt algebra. J Pure Appl Algebra, 1990, 68: 359–364
Su Y C. Harish-Chandra modules of the intermediate series over the high rank Virasoro algebras and high rank super-Virasoro algebras. J Math Phys, 1994, 35: 2013–2023
Su Y C. Classification of Harish-Chandra modules over the super-Virasoro algebras. Commun Algebra, 1995, 23: 3653–3675
Taft E J. Witt and Virasoro algebras as Lie bialgebras. J Pure Appl Algebra, 1993, 87: 301–312
Wu Y Z, Song G A, Su Y C. Lie bialgebras of generalized Virasoro-like type. Acta Math Sinica (English Ser), 2006, 22(6): 1915–1922
Wu Y Z, Song G A, Su Y C. Lie bialgebras of generalized Witt type. II. Comm Algebra, 2007, 35(6): 1992–2007
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Yang, H. Lie super-bialgebra structures on super-Virasoro algebra. Front. Math. China 4, 365–379 (2009). https://doi.org/10.1007/s11464-009-0012-x
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DOI: https://doi.org/10.1007/s11464-009-0012-x