Generalized polynomial modules over the Virasoro algebra
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- by Genqiang Liu and Yueqiang Zhao PDF
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Abstract:
Let $\mathcal {B}_r$ be the $(r+1)$-dimensional quotient Lie algebra of the positive part of the Virasoro algebra $\mathcal {V}$. Irreducible $\mathcal {B}_r$-modules were used to construct irreducible Whittaker modules in a work of Mazorchuk and Zhao (2014) and irreducible weight modules with infinite dimensional weight spaces over $\mathcal {V}$ in a work of Liu, Lu and Zhao (2015). In the present paper, we construct non-weight Virasoro modules $F(M, \Omega (\lambda ,\beta ))$ from irreducible $\mathcal {B}_r$-modules $M$ and $(\mathcal {A},\mathcal {V})$-modules $\Omega (\lambda ,\beta )$. We give necessary and sufficient conditions for the Virasoro module $F(M, \Omega (\lambda ,\beta ))$ to be irreducible. Using the weighting functor introduced by J. Nilsson, we also determine necessary and sufficient conditions for two $F(M, \Omega (\lambda ,\beta ))$ to be isomorphic.References
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Additional Information
- Genqiang Liu
- Affiliation: School of Mathematics and Statistics, Henan University, Kaifeng 475004, People’s Republic of China
- Email: liugenqiang@amss.ac.cn
- Yueqiang Zhao
- Affiliation: School of Mathematics and Statistics, Henan University, Kaifeng 475004, People’s Republic of China
- Email: yueqiangzhao@163.com
- Received by editor(s): December 16, 2015
- Received by editor(s) in revised form: February 16, 2016
- Published electronically: June 10, 2016
- Additional Notes: The first author was supported in part by the NSF of China (Grant 11301143) and grants at Henan University (2012YBZR031, yqpy20140044).
- Communicated by: Kailash C. Misra
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 5103-5112
- MSC (2010): Primary 17B10, 17B65, 17B66, 17B68
- DOI: https://doi.org/10.1090/proc/13171
- MathSciNet review: 3556256