Quasifinite modules of a Lie algebra related to Block type
Let \(\mathcal B\) be the Lie algebra, called a Lie algebra related to Block type, with basis \(\{L_{\alpha,i},\kappa\mid \alpha,i\in{\mathbb{Z}}\), \(i\geq0\}\) and relations \([L_{\alpha,i},L_{\beta,j}]=((i+1)\beta-(j+1)\alpha)L_{\alpha+\beta,i+j}+\delta_{\alpha+\beta,0}\delta_{i+j,0} \frac{\alpha^3-\alpha}{6}\kappa,\) \([\kappa,{\mathcal B}]=0\). The authors prove that any quasifinite irreducible \(\mathcal B\)-module is either highest weight, lowest weight or uniformly bounded. They also construct and classify the \(\mathcal B\)-modules of the intermediate series, and determine the necessary and sufficient condition for an irreducible highest weight module to be quasifinite.
scientific article; zbMATH DE number 5186650
scientific article