Two classes of Lie conformal superalgebras related to the Heisenberg--Virasoro Lie conformal algebra
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910722624061440 |
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| author | Wang, Jinrong Yue, Xiaoqing |
| author_facet | Wang, Jinrong Yue, Xiaoqing |
| contents | In this paper, firstly we construct two classes of Lie conformal superalgebras denoted by $\mathcal{HVS}(α)$ and $\mathcal{HVS}(β,γ,τ)$, respectively, where $α$ is an nonzero complex number and $β,γ,τ$ are complex numbers. They are both of rank $(2+1)$ and the even part $\mathcal{HVS}(α)_{\bar{0}}=\mathcal{HVS}(β,γ,τ)_{\bar{0}}$ is the Heisenberg--Virasoro Lie conformal algebra, which is a free $\mathbb{C}[\partial]$-module generated by $L$ and $H$ satisfying $[L_λL]=(\partial+2λ)L,\ [L_λH]=(\partial+λ)H,\ [H_λH]=0$. Then we completely determine the conformal derivations, conformal biderivations, automorphism groups and conformal modules of rank $(1+1)$ for these two Lie conformal superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two classes of Lie conformal superalgebras related to the Heisenberg--Virasoro Lie conformal algebra Wang, Jinrong Yue, Xiaoqing Rings and Algebras 17B10, 17B40, 17B65, 17B68 In this paper, firstly we construct two classes of Lie conformal superalgebras denoted by $\mathcal{HVS}(α)$ and $\mathcal{HVS}(β,γ,τ)$, respectively, where $α$ is an nonzero complex number and $β,γ,τ$ are complex numbers. They are both of rank $(2+1)$ and the even part $\mathcal{HVS}(α)_{\bar{0}}=\mathcal{HVS}(β,γ,τ)_{\bar{0}}$ is the Heisenberg--Virasoro Lie conformal algebra, which is a free $\mathbb{C}[\partial]$-module generated by $L$ and $H$ satisfying $[L_λL]=(\partial+2λ)L,\ [L_λH]=(\partial+λ)H,\ [H_λH]=0$. Then we completely determine the conformal derivations, conformal biderivations, automorphism groups and conformal modules of rank $(1+1)$ for these two Lie conformal superalgebras. |
| title | Two classes of Lie conformal superalgebras related to the Heisenberg--Virasoro Lie conformal algebra |
| topic | Rings and Algebras 17B10, 17B40, 17B65, 17B68 |
| url | https://arxiv.org/abs/2412.00735 |