arXiv subjects
Publications and source records attributed to Yan-an Cai.
In this paper, we classify all simple jet modules for contact superconformal algebras $\mathcal{K}(N;ε)$ with $N\neq4$. Then all simple quasifinite modules for $\widehat{\mathcal{K}}(N;ε)$ ($N\neq4$), the universal central extension of $\mathcal{K}(N;ε)$, are classified. Our results show that Matínez-Zelmanov's conjecture in \cite{MZe1} holds for $\mathcal{K}(N;ε)$ ($N\ne4$).
In this paper, we classify simple strong Harish-Chandra modules over the Lie superalgebra $W_{m,n}$ of vector fields on $\C^{m|n}$. Any such module is the unique simple submodule of some tensor module $F(P,V)$ for a simple weight module $P$ over the Weyl superalgebra $\mathcal K_{m,n}$ and a simple weight module $V$ over the general linear superalgebra $\gl_{m,n}$.
In this paper, we classify all simple jet modules for the Neveu-Schwarz algebra $\widehat{\mathfrak{k}}$ and its contact subalgebra $\mathfrak{k}^+$. Based on these results, we give a classification of simple Harish-Chandra modules for $\widehat{\mathfrak{k}}$ and $\mathfrak{k}^+$.
We classify Jet modules for the Lie (super)algebras $\mathfrak{L}=W\ltimes(\mathfrak{g}\otimes\mathbb{C}[t,t^{-1}])$, where $W$ is the Witt algebra and $\mathfrak{g}$ is a Lie superalgebra with an even diagonlizable derivation. Then we give a concept method to classify all simple cuspidal modules for $\mathfrak{L}$ and the map superalgebras, which are of the form $\mathfrak{L}\otimes R$, where $R$ is a Noetherian unital supercommutative associative superalgebra.
In the present paper, using the technique of localization, we determine the center of the quantum Schrödinger algebra $§_q$ and classify simple modules with finite-dimensional weight spaces over $§_q$, when $q$ is not a root of unity. It turns out that there are four classes of such modules: dense $U_q(\mathfrak{sl}_2)$-modules, highest weight modules, lowest weight modules, and twisted modules of highest weight modules.
Let $\g$ be an arbitrary Kac-Moody algebra with a Cartan sualgebra $\h$. In this paper, we determine the category of $\g$-modules that are free $U(\h)$-modules of rank 1.
A class of generalized Verma modules over $\fr{sl}_{n+2}$ is constructed from $\fr{sl}_{n+1}$-modules which are $\uhn$-free modules of rank $1$. The necessary and sufficient conditions for these $\fr{sl}_{n+2}$-modules to be simple are determined. This leads to a class of new simple $\fr{sl}_{n+2}$-modules.
In this paper, we construct a new class of modules for the Schrödinger algebra $\mS$, called quasi-Whittaker module. Different from \cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schrödinger algebra related with the triangular decomposition, but its Heisenberg subalgebra $\mH$. We prove that, for a simple $\mS$-module $V$, $V$ is a quasi-Whittaker module if and only if $V$ is a locally finite $\mH$-module; Furthermore, we classify the simple quasi-Whittaker modules by the elements with the action similar to the center elements in $U(\mS)$ and their quasi-Whittaker vectors. Finally, we characterize arbitrary quasi-Whittaker modules.