### Electronic Research Archive

2021, 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

• 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.

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

### Related Papers:

• 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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