Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra

Hongyan Guo; Hongyan Guo

doi:10.3934/era.2021008

Electronic Research Archive

2021, Volume 29, Issue 4: 2673-2685. doi: 10.3934/era.2021008

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Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra

Hongyan Guo

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received: 01 July 2020 Revised: 01 December 2020 Published: 11 January 2021
17B68, 17B69

We first determine the automorphism group of the twisted Heisenberg-Virasoro vertex operator algebra $ V_{\mathcal{L}}(\ell_{123},0) $. Then, for any integer $ t>1 $, we introduce a new Lie algebra $ \mathcal{L}_{t} $, and show that $ \sigma_{t} $-twisted $ V_{\mathcal{L}}(\ell_{123},0) $($ \ell_{2} = 0 $)-modules are in one-to-one correspondence with restricted $ \mathcal{L}_{t} $-modules of level $ \ell_{13} $, where $ \sigma_{t} $ is an order $ t $ automorphism of $ V_{\mathcal{L}}(\ell_{123},0) $. At the end, we give a complete list of irreducible $ \sigma_{t} $-twisted $ V_{\mathcal{L}}(\ell_{123},0) $($ \ell_{2} = 0 $)-modules.
- Automorphism group,
- twisted modules,
- twisted Heisenberg-Virasoro algebra
Citation: Hongyan Guo. Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra[J]. Electronic Research Archive, 2021, 29(4): 2673-2685. doi: 10.3934/era.2021008

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Abstract

We first determine the automorphism group of the twisted Heisenberg-Virasoro vertex operator algebra $ V_{\mathcal{L}}(\ell_{123},0) $. Then, for any integer $ t>1 $, we introduce a new Lie algebra $ \mathcal{L}_{t} $, and show that $ \sigma_{t} $-twisted $ V_{\mathcal{L}}(\ell_{123},0) $($ \ell_{2} = 0 $)-modules are in one-to-one correspondence with restricted $ \mathcal{L}_{t} $-modules of level $ \ell_{13} $, where $ \sigma_{t} $ is an order $ t $ automorphism of $ V_{\mathcal{L}}(\ell_{123},0) $. At the end, we give a complete list of irreducible $ \sigma_{t} $-twisted $ V_{\mathcal{L}}(\ell_{123},0) $($ \ell_{2} = 0 $)-modules.

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