Lie superbialgebra structures on the centerless twisted N=2 superconformal algebra

In this paper, Lie superbialgebra structures on the centerless twisted N=2 superconformal algebra \LL are considered which are proved to be coboundary triangular.Comment: 15 page

Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over the Twisted Schr\"{o}dinger-Virasoro Lie algebra

It is shown that the support of an irreducible weight module over the Schr\"{o}dinger-Virasoro Lie algebra with an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite-dimensional. As a side-product, it is obtained that every simple weight module over the Schr\"{o}dinger-Virasoro Lie algebra with a nontrivial finite-dimensional weight space, is a Harish-Chandra module.Comment: 6 page

Lie superbialgebra structures on the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra

Lie superbialgebra structures on the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra $\frak{tsns}$ are described. The corresponding necessary and sufficient conditions for such superbialgebra to be coboundary triangular are given. Meanwhile, the first cohomology group of $\frak{tsns}$ with coefficients in the tensor product of its adjoint module is completely determined

Leibniz Central Extension on the Twisted Schr\"{o}dinger-Virasoro Algebra

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.Comment: 9 page

The derivation algebra and automorphism group of the twisted Schr\"{o}dinger-Virasoro algebra

In this article, we determine the derivation algebra and the automorphism group of the twisted Schr\"{o}dinger-Virasoro algebra.Comment: 16 page

The Schr\"{o}dinger-Virasoro type Lie bialgebra: a twisted case

In this paper we investigate Lie bialgebra structures on a twisted Schr\"{o}dinger-Virasoro type algebra \LL. All Lie bialgebra structures on \LL are triangular coboundary, which is different from the relative result on the original Schr\"{o}dinger-Virasoro type Lie algebra. In particular, we find for this Lie algebra that there are more hidden inner derivations from itself to \LL\otimes\LL and we develop one method to search them.Comment: 14 page

Quantum group structure of the q-deformed WW algebra \WW_q

In this paper the q-deformed $W$ algebra \WW_q is constructed, whose nontrivial quantum group structure is presented.Comment: 7 page

Classification of modules of the intermediate series over the twisted N=2 superconformal algebra

In this paper, a classification of modules of the intermediate series over the twisted N=2 superconformal algebra is obtained.Comment: 1

Lie super-bialgebra structures on a class of generalized super WW-algebra L\mathfrak{L}

In this paper, Lie super-bialgebra structures on a class of generalized super $W$-algebra $\mathfrak{L}$ are investigated. By proving the first cohomology group of $\mathfrak{L}$ with coefficients in its adjoint tensor module is trivial, namely, $H^1(\mathfrak{L},\mathfrak{L}\otimes {\mathfrak{L}})=0$, we obtain that all Lie super-bialgebra structures on $\mathfrak{L}$ are triangular coboundary

Derivations and automorphisms of twisted deformative Schr\"{o}dinger-Virasoro Lie algebras

In this paper the derivation algebra and automorphism group of the twisted deformative Schr\"{o}dinger-Virasoro Lie algebras are determined.Comment: 25 page