arXiv subjects
Publications and source records attributed to Huanxia Fa.
In paper, we study the representation theory of super $W(2,2)$ algebra ${\mathfrak{L}}$. We prove that ${\mathfrak{L}}$ has no mixed irreducible modules and give the classification of irreducible modules of intermediate series. We determinate the conjugate-linear anti-involution of ${\mathfrak{L}}$ and give the unitary modules of intermediate series.
In this paper, the derivation algebras and automorphism groups of a class of deformative super $W$-algebras $W_{\lambda}(2,2)$ are determined.
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.
It is shown that there are no simple mixed modules over the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra, which implies that every irreducible weight module over it with a nontrivial finite-dimensional weight space, is a Harish-Chandra module.
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.
In this paper, we determine the derivation algebra and automorphism group of the twisted N=2 superconformal algebra. Then we generalize the relative results to the generalized twisted N=2 superconformal algebra in the final section.
In this paper we investigate Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras mainly using the techniques introduced recently by Liu, Pei and Zhu, which indicate that all cases considered in this paper except one behave different from their centerless ones.
In the present paper we shall determine all the non-degenerate symmetric invariant bilinear forms on the deformative Schrödinger-Virasoro algebras.
In this paper we investigate Lie bialgebra structures on a twisted Schrödinger-Virasoro type algebra $\LL$. All Lie bialgebra structures on $\LL$ are triangular coboundary, which is different from the relative result on the original Schrödinger-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.
In this paper, Lie superbialgebra structures on the centerless twisted N=2 superconformal algebra $\LL$ are considered which are proved to be coboundary triangular.
Lie superbialgebra structures on the centerless topological N=2 superconformal algebra $\TT$ are considered, all of which are proved to be coboundary triangular.
In this paper the q-deformed $W$ algebra $\WW_q$ is constructed, whose nontrivial quantum group structure is presented.