arXiv subjects
Publications and source records attributed to Qiufan Chen.
The present paper is devoted to study 2-local derivations on the Block-type Lie algebra which is an infinite-dimensional Lie algebra with some outer derivations. We prove that every 2-local derivation on the Block-type Lie algebra is a derivation.
In this paper, we construct and classify a class of non-weight modules over the BMS-Kac-Moody algebra, which are free modules of rank one when restricted to the universal enveloping algebra of the Cartan subalgebra (modulo center). We give the classification of such modules. Moreover, the irreducibility and the isomorphism classes of these modules are determined.
In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras, and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras including finite-dimensional simple Lie algebras over arbitrary fields of characteristic not $2$ or $3$, and the Witt algebras $\mathcal{W}^+_n$ over fields of characteristic $0$. As an application, commutative post-Lie algebra structure on aforementioned Lie algebras is shown to be trivial.
Irreducibilities of Verma modules over a class of Block type Lie algebras are completely determined. The approach developed in the present paper can be used to deal with non-weight modules.
Let $\mathcal{G}$ be the planar Galilean conformal algebra and $\widetilde{\mathcal{G}}$ be its universal central extension. Then $\mathcal{G}$ (resp. $\widetilde{\mathcal{G}}$) admits a triangular decomposition: $\mathcal{G}=\mathcal{G}^{+}\oplus\mathcal{G}^{0}\oplus\mathcal{G}^{-}$ (resp. $\widetilde{\mathcal{G}}=\widetilde{\mathcal{G}}^{+}\oplus\widetilde{\mathcal{G}}^{0}\oplus\widetilde{\mathcal{G}}^{-}$). In this paper, we study universal and generic Whittaker $\mathcal{G}$-modules (resp. $\widetilde{\mathcal{G}}$-modules) of type $ϕ$, where $ϕ:\mathcal{G}^{+}=\widetilde{\mathcal{G}}^{+}\longrightarrow\mathbb{C}$ is a Lie algebra homomorphism. We classify the isomorphism classes of universal and generic Whittaker modules. Moreover, we show that a generic Whittaker modules of type $ϕ$ is irreducible if and only if $ϕ$ is nonsingular. For the nonsingular case, we completely determine the Whittaker vectors in universal and generic Whittaker modules. For the singular case, we concretely construct some proper submodules of generic Whittaker modules.
In this paper, we study a class of non-weight modules over the affine-Virasoro algebra of type $A_1$, which are free modules of rank one when restricted to the Cartan subalgebra (modulo center). We give the classification of such modules. Moreover, the simplicity and the isomorphism classes of these modules are determined.
In this paper, a new class of $\Z$-graded Lie conformal algebras $\CW(a,c)$ of infinite rank is constructed. The conformal derivations and one-dimensional central extensions of $\CW(a,c)$ are completely determined. And all conformal modules of rank one over $\CW(a,c) (a\neq0)$ are proved to be trivial and all such nontrivial (irreducible) modules over $\CW(0,c)$ are classified.
For any two complex numbers $a$ and $b$, $\mathcal{V} ir(a,b)$ is a central extension of $\mathcal{W}(a,b)$ which is universal in the case $(a,b)\neq (0,1)$, where $\mathcal{W}(a,b)$ is the Lie algebra with basis $\{L_n,W_n\mid n\in\Z\}$ and relations $[L_m,L_n]=(n-m)L_{m+n}$, $[L_m,W_n]=(a+n+bm)W_{m+n}$, $[W_m,W_n]=0$. In this paper, we construct and classify a class of non-weight modules over the algebra $\mathcal{V} ir(a,b)$ which are free $U(\mathbb{C} L_0\oplus\mathbb{C} W_0)$-modules of rank $1$. It is proved that such modules can only exist for $a=0$.
In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Virasoro algebras. In particular,the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.
The Lie conformal algebra of loop Virasoro algebra, denoted by $\mathscr{CW}$, is introduced in this paper. Explicitly, $\mathscr{CW}$ is a Lie conformal algebra with $\mathbb{C}[\partial]$-basis $\{L_i\,|\,i\in\mathbb{C}\}$ and $λ$-brackets $[L_i\, {}_λ\, L_j]=(-\partial-2λ) L_{i+j}$. Then conformal derivations of $\mathscr{CW}$ are determined. Finally, rank one conformal modules and $\mathbb{Z}$-graded free intermediate series modules over $\mathscr{CW}$ are classified.