Non-weight modules over algebras related to the Virasoro algebra

作者：Chen, Qiu-Fan; Yao, Yu-Feng^*

来源：Journal of Geometry and Physics, 2018, 134: 11-18.

DOI：10.1016/j.geomphys.2018.08.002

• Virasoro algebra
• Loop-Virasoro algebra
• Block type Lie algebra
• Non-weight module
• Simple module

In this paper, we study some non-weight modules over the loop-Virasoro algebra (sic) and Block type Lie algebras B(q), where q is a nonzero complex number. Those modules when restricted to the Cartan subalgebra (modulo center) are free of rank one. We provide a sufficient and necessary condition for such modules to be simple, and determine their isomorphism classes. Moreover, we obtain the simplicity of modules over loop-Virasoro algebras by taking tensor products of some irreducible modules mentioned above with irreducible highest weight modules or Whittaker modules.

• 出版日期2018-12
• 单位上海海事大学