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Classification of finite irreducible conformal modules over Lie conformal algebra $ \mathcal{W}(a, b, r) $

  • Received: 01 May 2020 Revised: 01 October 2020 Published: 24 November 2020
  • 17B10, 17B65, 17B68

  • We study a family of non-simple Lie conformal algebras $ \mathcal{W}(a,b,r) $ ($ a,b,r\in {\mathbb{C}} $) of rank three with free $ {\mathbb{C}}[{\partial}] $-basis $ \{L, W,Y\} $ and relations $ [L_{\lambda} L] = ({\partial}+2{\lambda})L,\ [L_{\lambda} W] = ({\partial}+ a{\lambda} +b)W,\ [L_{\lambda} Y] = ({\partial}+{\lambda})Y,\ [Y_{\lambda} W] = rW $ and $ [Y_{\lambda} Y] = [W_{\lambda} W] = 0 $. In this paper, we investigate the irreducibility of all free nontrivial $ \mathcal{W}(a,b,r) $-modules of rank one over $ {\mathbb{C}}[{\partial}] $ and classify all finite irreducible conformal modules over $ \mathcal{W}(a,b,r) $.

    Citation: Wenjun Liu, Yukun Xiao, Xiaoqing Yue. Classification of finite irreducible conformal modules over Lie conformal algebra $ \mathcal{W}(a, b, r) $[J]. Electronic Research Archive, 2021, 29(3): 2445-2456. doi: 10.3934/era.2020123

    Related Papers:

  • We study a family of non-simple Lie conformal algebras $ \mathcal{W}(a,b,r) $ ($ a,b,r\in {\mathbb{C}} $) of rank three with free $ {\mathbb{C}}[{\partial}] $-basis $ \{L, W,Y\} $ and relations $ [L_{\lambda} L] = ({\partial}+2{\lambda})L,\ [L_{\lambda} W] = ({\partial}+ a{\lambda} +b)W,\ [L_{\lambda} Y] = ({\partial}+{\lambda})Y,\ [Y_{\lambda} W] = rW $ and $ [Y_{\lambda} Y] = [W_{\lambda} W] = 0 $. In this paper, we investigate the irreducibility of all free nontrivial $ \mathcal{W}(a,b,r) $-modules of rank one over $ {\mathbb{C}}[{\partial}] $ and classify all finite irreducible conformal modules over $ \mathcal{W}(a,b,r) $.



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