Acta mathematica scientia, Series B >
LIE SUPER-BIALGEBRA STRUCTURES |ON GENERALIZED SUPER-VIRASORO ALGEBRAS
Received date: 2006-12-21
Revised date: 2008-03-07
Online published: 2010-01-20
Supported by
Supported by the Foundation of Shanghai Education Committee (06FZ029), NSF of China (10471091), ``One Hundred Program'' from University of Science and Technology of China.
In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras L are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if H1(L, L{\cal L})=0.
YANG Heng-Yun , SU Yu-Cai . LIE SUPER-BIALGEBRA STRUCTURES |ON GENERALIZED SUPER-VIRASORO ALGEBRAS[J]. Acta mathematica scientia, Series B, 2010 , 30(1) : 225 -239 . DOI: 10.1016/S0252-9602(10)60040-9
[1] Ademollo M, et al. Supersymmetric strings and colour confinement. Phys Lett B, 1976, 62: 105
[2] Drinfeld V G. Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang-Baxter equations. (Russian) Dokl Akad Nauk SSSR, 1983, 268: 285--287
[3] Drinfeld V G. Quantum groups//Proceeding of the International Congress of Mathematicians, Vol 1, 2. Providence, RI: Amer Math Soc, 1987: 798--820
[4] Kac V G, van de Leuer J W. On classification of superconformal algebras//Gates S J. Strings 88. Sinapore: World Scientific, 1988: 77--106
[5] Kac V G. Superconformal algebras and transitive groups actions on quadrics. Commun Math Phys, 1997, 186: 233--252
[6] Michaelis W. A class of infinite-dimensional Lie bialgebras containing the Virasoro algebras. Adv Math, 1994, 107: 365--392
[7] 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
[8] Nichols W D. The structure of the dual Lie coalgebra of the Witt algebra. J Pure Appl Algebra, 1990, 68: 395--364
[9] Taft E J. Witt and Virasoro algebras as Lie bialgebras. J Pure Appl Algebra, 1993, 87: 301--312
\REF{
[10]} Patera J, Zassenhaus H. The higher rank Virasoro algebras.
Commun Math Phys, 1991, {\bf 36}: 1--14
\REF{
[11]} 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, {\bf 35}: 2013--2023
\REF{
[12]} Su Y C. Simple modules over the high rank Virasoro
algebras.
Commun Algebra, 2001, {\bf 29}: 2067-2080
\REF{
[13]} Su Y C. Classification of Harish-Chandra modules over the
higher rank Virasoro algebras. Commun Math Phys, 2003, {\bf 240}: 539--551
\REF{
[14]} Su Y C, Zhao K M. Generalized Virasoro and super-Virasoro
algebras and modules of intermediate series. J Algebra, 2002, {\bf 252}: 1--19
\REF{
[15]} Wu Y Z, Song G A, Su Y C. Lie bialgebras of generalized
Witt type $\Pi$. Commun Algebra, 2007, {\bf 3}: 1992--2007
\REF{
[16]} Wu Y Z, Song G A, Su Y C. Lie bialgebras of generalized
Virasoro-like type. Acta Math Sinica (English Series), 2006, {\bf 22}: 1915--1922
/
| 〈 |
|
〉 |