Related papers: The Schr\"{o}dinger-Virasoro type Lie bialgebra: a…
In this paper we investigate Lie bialgebra structures on the Schr\"odinger-Virasoro algebra $\LL$. Surprisingly, we find out an interesting fact that not all Lie bialgebra structures on the Schr\"odinger-Virasoro algebra are triangular…
In this paper we investigate Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra. With the classifications of Lie bialgebra structures on the Virasoro algebra, we determined such structures on the twisted Heisenberg-Virasoro…
In two recent papers by the authors, all Lie bialgebra structures on Lie algebras of generalized Witt type are classified. In this paper all Lie bialgebra structures on generalized Virasoro-like algebras are determined. It is proved that…
In this paper we investigate Lie bialgebra structures on the deformative Schr\"{o}dinger-Virasoro algebras mainly using the techniques introduced recently by Liu, Pei and Zhu, which indicate that all cases considered in this paper except…
In this paper, Lie bialgebra structures on the extended Schrodinger-Virasoro Lie algebra are classified. It is obtained that all the Lie bialgebra structures on L are triangular coboundary. As a by-product, it is derived that the first…
In this paper, we characterize the biderivations of Schr\"odinger-Virasoro Lie algebra. We get a classes of non-inner and non-skewsymmetric biderivations. As application, we characterize the commutative post-Lie algebra structures on…
In this paper, Lie bialgebra structures on generalized Heisenberg-Virasoro algebra $\mathfrak{L}$ are considered. Also, $H^1({\mathfrak{L}} ,\mathfrak{L}\bigotimes\mathfrak{L})$ is given explicitly. Moreover, it is proved that all Lie…
In this paper the derivation algebra and automorphism group of the twisted deformative Schr\"{o}dinger-Virasoro Lie algebras are determined.
In this paper, Lie superbialgebra structures on the centerless twisted N=2 superconformal algebra $\LL$ are considered which are proved to be coboundary triangular.
In this paper, by studying the maximal good subspaces, we determine the dual Lie coalgebras of the centerless twisted Heisenberg-Virasoro algebra. Based on this, we construct the dual Lie bialgebras structures of the twisted…
In the present paper we shall investigate the Lie bialgebra structures on the Lie algebra $\widetilde{\frak{sl}_2(C_q[x,y])}$, which are shown to be triangular coboundary.
Structures of dual Lie bialgebras on the one sided Witt algebra, the Witt algebra and the Virasoro algebra are investigated. As a result, we obtain some infinite dimensional Lie algebras.
In this article, we determine the derivation algebra and the automorphism group of the twisted Schr\"{o}dinger-Virasoro algebra.
Lie bialgebra structures on the extended affine Lie algebra $\widetilde{sl_2(\mathbb{C}_q)}$ are investigated. In particular, all Lie bialgebra structures on $\widetilde{sl_2(\mathbb{C}_q)}$ are shown to be triangular coboundary. This…
We introduce and study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfeld double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the algebraic structure of the triple,…
The first cohomology group of a generalized loop Virasoro algebra with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is applied to prove that Lie bialgebra structures on generalized loop…
Verma modules over the $W$-algebra W(2,2) were considered by Zhang and Dong, while the Harish-Chandra modules and irreducible weight modules over the same algebra were classified by Liu and Zhu etc. In the present paper we shall investigate…
In this paper, we introduce two kinds of Lie conformal algebras associated with the loop Schr\"odinger-Virasoro Lie algebra and the extended loop Schr\"odinger-Virasoro Lie algebra, respectively. The conformal derivations, the second…
In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras…
In this paper we present all the Leibniz 2-cocycles of the twisted Schr\"{o}dinger-Virasoro algebra, which determine its second Leibniz cohomology group.