American Institute of Mathematical Sciences

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2688-1594

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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

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.

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}.

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.

2021, 29(5): 2945-2957 doi: 10.3934/era.2021020 +[Abstract](15)+[HTML](11) +[PDF](303.23KB)
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2021, 29(6): 3741-3760 doi: 10.3934/era.2021059 +[Abstract](15)+[HTML](11) +[PDF](383.89KB)
Abstract:
2021, 29(6): 3909-3993 doi: 10.3934/era.2021068 +[Abstract](15)+[HTML](11) +[PDF](655.29KB)
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2020 Impact Factor: 1.833
5 Year Impact Factor: 1.833