arXiv subjects

Yuezhu Wu

Publications and source records attributed to Yuezhu Wu.

7 recordsLinked to original sources

arXiv2026

Simple Restricted modules for $N=2$ Neveu-Schwarz algebra

In this paper, we first construct many simple restricted modules for the $N=2$ Neveu-Schwarz algebra $\mathcal{L}$. These modules contain the highest weight modules and Whittaker modules. Then we precisely characterize the simple restricted modules over $\mathcal{L}$ under certain conditions, and establish several equivalent conditions for a simple $\mathcal{L}$-module to be restricted. Finally, we prove that if one specific positive root element of $\mathcal{L}$ acts locally finitely on a simple $\mathcal{L}$-module $V$, then $V$ must be restricted.

math.RT↗

arXiv2014

Integrable representations of the quantum affine special linear superalgebra

The simple integrable modules with finite dimensional weight spaces are classified for the quantum affine special linear superalgebra $\U_q(\hat{\mathfrak{sl}}(M|N))$ at generic $q$. Any such module is shown to be a highest weight or lowest weight module with respect to one of the two natural triangular decompositions of the quantum affine superalgebra depending on whether the level of the module is zero or not. Furthermore, integrable $\U_q(\hat{\mathfrak{sl}}(M|N))$-modules at nonzero levels exist only if $M$ or $N$ is $1$.

math.RT↗

arXiv2014

Integrable representations of affine A(m, n) and C(m) superalgebras

Rao and Zhao classified the irreducible integrable modules with finite dimensional weight spaces for the untwisted affine superalgebras which are not $\hat{A}(m,n)$ ($m\ne n$) or $\hat{C}(m)$. Here we treat the latter affine superalgebras to complete the classification. The problem boils down to classifying the irreducible zero-level integrable modules with finite dimensional weight spaces for these affine superalgebras, which is solved in this paper. We note in particular that such modules for $\hat{A}(m,n)$ ($m\ne n$) and $\hat{C}(m)$ must be of highest weight type, but are not necessarily loop modules. This is in sharp contrast to the cases of ordinary affine algebras and the other types of affine superalgebras.

math.RT↗

arXiv2006

Quantization of generalized Virasoro-like algebras

In a recent paper by the authors, Lie bialgebras structures of generalized Virasoro-like type were considered. In this paper, the explicit formula of the quantization of generalized Virasoro-like algebras is presented.

math.QA↗

arXiv2006

Lie bialgebras of generalized Virasoro-like type

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 all such Lie bialgebras are triangular coboundary.

math.AG↗

arXiv2006

Verma modules over a Block Lie algebra

Let B be the Lie algebra with basis {L_{i,j},C|i,j\in Z} and relations [L_{i,j},L_{k,l}]=((j+1)k-i(l+1))L_{i+k,j+l}+iδ_{i,-k}δ_{j+l,-2}C, [C,L_{i,j}]=0. It is proved that an irreducible highest weight B-module is quasifinite if and only if it is a proper quotient of a Verma module. For an additive subgroup G of the base field F, there corresponds to a Lie algebra B(G) of Block type. Given a totalorder \succ on G and a weight Λ, a Verma B(G)-module M(Λ,\succ) is defined. The irreducibility of M(Λ,\succ) is completely determined.

math.RT↗

arXiv2005

Highest weight representations of a Lie algebra of Block type

For a field $F$ of characteristic zero and an additive subgroup $G$ of $F$, a Lie algebra $B(G)$ of lock type is defined with basis $\{L_{a,i},c|a \in G, i>-2\}$ and relations $[L_{a,i},L_{b,j}]=((i+1)b-(j+1)a)L_{a+b,i+j}+a\d_{a,-b}\d_{i+j,-2}c, [c,L_{a,i}]=0.$ Given a total order $\succ$ on $G$ compatible with its group structure, and any $Λ\in B(G)_0^*$, a Verma $B(G)$-module $M(Λ,\succ)$ is defined, and the irreducibility of $M(Λ,\succ)$ is completely determined. Furthermore, it is proved that an irreducible highest weight $B(Z)$-module is quasifinite if and only if it is a proper quotient of a Verma module.

math.QA↗