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Special issue on vertex algebras, lie algebras, and related topics

Ching Hung Lam, Academia Sinica, Taiwan chlam@math.sinica.edu.tw

Haisheng Li, Rutgers University, Camden, USA hli@camden.rutgers.edu

Qiang Mu, Harbin Normal University, China qmu520@gmail.com

Solvability of the matrix equation $ AX^{2} = B $ with semi-tensor productSpecial Issues
Jin Wang, Jun-E Feng and Hua-Lin Huang
2021, 29(3): 2249-2267 doi: 10.3934/era.2020114 +[Abstract](633)+[HTML](325) +[PDF](418.13KB)
Abstract:

We investigate the solvability of the matrix equation \begin{document}$ AX^{2} = B $\end{document} in which the multiplication is the semi-tensor product. Then compatible conditions on the matrices \begin{document}$ A $\end{document} and \begin{document}$ B $\end{document} are established in each case and necessary and sufficient condition for the solvability is discussed. In addition, concrete methods of solving the equation are provided.

Classification of finite irreducible conformal modules over Lie conformal algebra $ \mathcal{W}(a, b, r) $Special Issues
Wenjun Liu, Yukun Xiao and Xiaoqing Yue
2021, 29(3): 2445-2456 doi: 10.3934/era.2020123 +[Abstract](598)+[HTML](268) +[PDF](330.24KB)
Abstract:

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

Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebraSpecial Issues
Hongyan Guo
2021, 29(4): 2673-2685 doi: 10.3934/era.2021008 +[Abstract](430)+[HTML](198) +[PDF](337.68KB)
Abstract:

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

Structure of sympathetic Lie superalgebrasSpecial Issues
Yusi Fan, Chenrui Yao and Liangyun Chen
2021,  doi: 10.3934/era.2021020 +[Abstract](15)+[HTML](11) +[PDF](303.23KB)
Abstract:
Constructions of three kinds of Bihom-superalgebrasSpecial Issues
Ying Hou and Liangyun Chen
2021,  doi: 10.3934/era.2021059 +[Abstract](15)+[HTML](11) +[PDF](383.89KB)
Abstract:
The algebraic classification of nilpotent commutative algebrasSpecial Issues
Doston Jumaniyozov, Ivan Kaygorodov and Abror Khudoyberdiyev
2021,  doi: 10.3934/era.2021068 +[Abstract](15)+[HTML](11) +[PDF](655.29KB)
Abstract:

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