Lie super-bialgebra structures on super-Virasoro algebra

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.

Keywords

Lie super-bialgebra / Yang-Baxter equation / super-Virasoro algebra

References

[1] 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)

[2] 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

[3] Michaelis W. A class of infinite-dimensional Lie bialgebras containing the Virasoro algebras. Adv Math, 1994, 107: 365-392

[4] 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

[5] Nichols W D. The structure of the dual Lie coalgebra of the Witt algebra. J Pure Appl Algebra, 1990, 68: 359-364

[6] 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

[7] Su Y C. Classification of Harish-Chandra modules over the super-Virasoro algebras. Commun Algebra, 1995, 23: 3653-3675

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

[9] 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

[10] 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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