Generalized Virasoro Operators

Abstract

We define generalized Virasoro operators acting on a Fock space V(Γ). These generalize the standard construction of Virasoro operators. By using the Jacobi Identity we compute the commutators of these operators. These operators result in an abelian extension of the toroidal Lie algebra. We explicitly describe the abelian extension.

Key Words:

• Virasoro operators
• Fock space
• Jacobi identity

Mathematics Subject Classification:

• Primary 17B69
• Secondary 17B68, 17B65, 17B66

Notes

^#Communicated by E. Zelmanov.