Indecomposable modules of the intermediate series over W(a,b) algebras
Representation Theory
2012-10-29 v2
Abstract
For any complex parameters a,b, the W(a,b) algebra is the Lie algebra with basis {L_i,W_i|i\in Z}, and relations [L_i,L_j]=(j-i)L_{i+j}, [L_i,W_j]=(a+j+bi)W_{i+j},[W_i,W_j]=0. In this paper, indecomposable modules of the intermediate series over W(a,b) are classified. It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module. Furthermore, if a\notin Q, an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of W_k.
Keywords
Cite
@article{arxiv.1103.3850,
title = {Indecomposable modules of the intermediate series over W(a,b) algebras},
author = {Yucai Su and Ying Xu and Xiaoqing Yue},
journal= {arXiv preprint arXiv:1103.3850},
year = {2012}
}
Comments
24 pages