Integrable representations for generalized Virasoro-toroidal Lie algebras.
Let \(V\) be an irreducible integrable module over a generalized Virasoro-toroidal Lie algebra \(\mathfrak{g}\). In this paper it is shown that if \(M\) has finite-dimensional weight spaces and a non-zero central charge, then \(M\cong L(\Lambda)\otimes \overline{M}\), where \(L(\Lambda)\) is an irreducible highest (or lowest) weight module for an appropriate affine Lie algebra, associated with \(\mathfrak{g}\), and \(\overline{M}\) is an irreducible module over the centrally extended subalgebra of full derivations of \(\mathfrak{g}\) with finite-dimensional weight spaces and the same central charge.
scientific article; zbMATH DE number 2026930
scientific article