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On a Class of Infinite Simple Lie Conformal Algebras

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Abstract

In this paper, we study a class of infinite simple Lie conformal algebras associated to a class of generalized Block type Lie algebras. The central extensions by a one-dimensional center \(\mathbb {C}\mathfrak {c}\), conformal derivations and free intermediate series modules of this class of Lie conformal algebras are determined. Moreover, we also show that these Lie conformal algebras do not have any non-trivial finite conformal modules. Consequently, these Lie conformal algebras cannot be embedded into gcN for any positive integer N.

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Acknowledgements

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (No. LY20A010022), CSC (No. 202008310011), University Natural Science Research Project of Anhui Province under Grant (No. KJ2019A0845), the Scientific Research Foundation of Hangzhou Normal University (No. 2019QDL012) and the National Natural Science Foundation of China (No. 11871421, 11501515, 11801369). We wish to thank the referee for careful reading and useful comments. In particular, we would like to thank the referee for giving Lemmas 5.1 and 6.4 to improve the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 311121, People’s Republic of China

    Yanyong Hong

  2. Department of Mathematics and Physics, Hefei University, Hefei, 230601, People’s Republic of China

    Yang Pan

  3. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201209, People’s Republic of China

    Haibo Chen

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  1. Yanyong Hong
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  2. Yang Pan
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  3. Haibo Chen
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Correspondence to Yang Pan.

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Presented by: Iain Gordon

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Hong, Y., Pan, Y. & Chen, H. On a Class of Infinite Simple Lie Conformal Algebras. Algebr Represent Theor 25, 801–822 (2022). https://doi.org/10.1007/s10468-021-10047-9

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