Classification of simple bounded weight modules of the Lie algebra of vector fields on $\C^n$

Abstract

Let $W_n^{+}$ be the Lie algebra of the Lie algebra of vector fields on $\C^n$. In this paper, we classify all simple bounded weight $W_n^{+}$ modules. Any such module is isomorphic to the simple quotient of a tensor module $F(P,M)=P\otimes M$ for a simple weight module $P$ over the Weyl algebra $K_n^{+}$ and a finite dimensional simple $\gl_n$ module $M$.

References in corpus (1)

• Simple weight modules with finite-dimensional weight spaces over Witt superalgebras

Cited by in corpus (4)

• Simple weight modules with finite-dimensional weight spaces over Witt superalgebras
• bounded weight modules over the Lie superalgebra of Cartan W-type
• Classification of simple Harish-Chandra modules over the Neveu-Schwarz algebra and its contact subalgebra
• Classification of simple strong Harish-Chandra modules over the Lie superalgebra of vector fields on $\C^{m|n}$