$(n+1)$维时空中Schr{ö}dinger李代数的局部导子

第n个薛定谔代数上的局部导子

Local derivation on the $n$-th Schr{ö}dinger algebra

本文研究第n个薛定谔代数上的局部导子，证明了其上的每个局部导子都是导子。

Irreducible weight modules over the Schr{ö}dinger Lie algebra in $(n+1)$ dimensional space-time

In this paper, we study weight representations over the Schr{ö}dinger Lie algebra $\mathfrak{s}_n$ for any positive integer $n$. It turns out that the algebra $\mathfrak{s}_n$ can be realized by polynomial differential operators. Using this realization, we give a complete classification of irreducible weight $\mathfrak{s}_n$-modules with finite dimensional weight spaces for any $n$. All such modules can be clearly characterized by the tensor product of $\mathfrak{so}_n$-modules, $\mathfrak{sl}_2$-modules and modules over the Weyl algebra.