arXiv subjects
Publications and source records attributed to Shoulan Gao.
In this paper, we classify 1-cocycles of the Witt algebra with coefficients in the tensor product of two arbitrary tensor density modules. In a special case, we recover a theorem originally established by Ng and Taft in \cite{NT}. Furthermore, by these 1-cocycles, we determine Lie bialgebra structures over certain infinite-dimensional Lie algebras containing the Witt algebra.
This paper aims to study the local derivations, 2-local automorphisms and local automorphisms on the super-Virasoro algebras. The primary focus is to establish that every local derivation of the super-Virasoro algebras is indeed a derivation, and to demonstrate that every local or 2-local automorphism of the super-Virasoro algebras is an automorphism.
In this paper, we consider some non-weight modules over the Lie algebra of Weyl type. First, we determine the modules whose restriction to $U(\frak h)$ are free of rank $1$ over the Lie algebra of differential operators on the circle. Then we determine the necessary and sufficient conditions for the tensor products of quasi-finite highest weight modules and $U(\frak h)$-free modules to be irreducible, and obtain that any two such tensor products are isomorphic if and only if the corresponding highest weight modules and $U(\frak h)$-free modules are isomorphic. Finally, we extend such results to the Lie algebras of differential operators in the general case.
The present paper is devoted to studying local derivations on the Lie algebra $W(2,2)$ which has some outer derivations. Using some linear algebra methods in \cite{CZZ} and a key construction for $W(2,2)$ we prove that every local derivation on $W(2, 2)$ is a derivation. As an application, we determine all local derivations on the deformed $\mathfrak{bms}_3$ algebra.
In this paper, all symmetric super-biderivations of some Lie superalgebras are determined. As an application, commutative post-Lie superalgebra structures on these Lie superalgebras are also obtained.
The present paper is devoted to study 2-local superderivations on the super Virasoro algebra and the super W(2,2) algebra. We prove that all 2-local superderivations on the super Virasoro algebra as well as the super W(2,2) algebra are (global) superderivations.
In this paper, we study the derivations, central extensions and the automorphisms of the infinite-dimensional Lie algebra W which appeared in [8] and Dong-Zhang's recent work [22] on the classification of some simple vertex operator algebras.
We show that the support of an irreducible weight module over the $W$-algebra $W(2, 2)$, which has 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 corollary, we obtain that every irreducible weight module over the the $W$-algebra $W(2, 2)$, having a nontrivial finite dimensional weight space, is a Harish-Chandra module (and hence is either an irreducible highest or lowest weight module or an irreducible module of the intermediate series).
In this paper, we study the derivations, the central extensions and the automorphism group of the extended Schrodinger-Virasoro Lie algebra, introduced by J. Unterberger in the context of two-dimensional conformal field theory and statistical physics. Moreover, we show that the extended Schrodinger-Virasoro Lie algebra is an infinite-dimensional complete Lie algebra and the universal central extension of the extended Schrodinger-Virasoro Lie algebra in the category of Leibniz algebras is the same as that in the category of Lie algebras.
It is proved that an irreducible module over the non-graded Virasoro-like algebra, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, the classification of some uniformly bounded modules is given.