The higher rank Virasoro algebras
The generalized Virasoro algebra V(M/F) as central extension of the Lie algebra L(M/F) is studied, where F denotes a field of arbitrary characteristic and M is a finite submodule of F. The additive orderings of M are used to study the structure and the representations of the generalized Virasoro algebras in the case of characteristic zero. Every additive ordering gives rise to a triangular decomposition of V(M/F). The automorphism group is characterized as a semidirect product (Theorem 3). The finite dimensional subalgebras are listed (Theorem 4). Verma modules and unitary Verma representation spaces are defined in the case that M is a vector lattice in the complex plane. There are six examples illustrating the considerations.
scientific article; zbMATH DE number 4212280
scientific article