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arXiv · 1802.01814

Non-weight modules over algebras related to the Virasoro algebra

Qiu-Fan Chen·Yu-Feng Yao
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Abstract

In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras $\mathfrak{L}$ and a class of Block type Lie algebras $\mathfrak{B(q)}$, where $q$ is a nonzero complex number. We determine those modules whose restriction to the Cartan subalgebra (modulo center) are free of rank one. We also 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.

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BibTeXRIS

Qiu-Fan Chen, Yu-Feng Yao. 2018-02-06. Non-weight modules over algebras related to the Virasoro algebra. https://doi.org/10.1016/j.geomphys.2018.08.002

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