In this paper, we first discuss the structure of the Ramond N = 2 superconformal algebras. Then we classify the modules of the intermediate series over Ramond N = 2 superconformal algebra.

The fusion rules for vertex operator algebra V A4 L2 are determined.

An explicit construction of indecomposable modules for the twisted Heisenberg-Virasoro algebra and representations for the full toroidal Lie algebras are given.

Abstract. For any additive subgroup G of an arbitrary field F of characteristic zero, there corresponds a generalized Heisenberg-Virasoro algebra L [G]. Given a total order of G compatible with its group structure, and any h, h I , c, cis defined. In the this note, the irreducibility of Verma modules M (h, h I , c, c I , c LI ) is completely determined.

In this paper, we study Verma modules for the twisted affine Nappi-Witten algebras \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}[\tau _{1}]$\end{document}Ĥ4[τ1] and \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}[\tau _{2}]$\end{document}Ĥ4[τ2]. The vertex operator representations of the affine Nappi-Witten algebras \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}[\tau _{1}]$\end{document}Ĥ4[τ1], \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}[\tau _{2}]$\end{document}Ĥ4[τ2], and \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}$\end{document}Ĥ4 are also constructed. Furthermore, the irreducible non-zero level quasifinite modules over the affine Nappi-Witten algebras are classified.