Z × Z-GRADED LIE ALGEBRAS CONTAINING A VIRASORO ALGEBRA AND A HEISENBERG ALGEBRA

Abstract

Let Z be the ring of integers. In this paper we classify Z × Z-graded Lie algebras A = i, j∈Z A i, j over a characteristic 0 field F with dim A i, j ≤ 1 for each i and j, satisfying the following three properties: I. A 0 = i∈Z A i, 0 ≃ Vir, the centerless Virasoro algebra; II. A 0,−1, A 0,0, A 0,1 span a Heisenberg algebra; III. A is generated by the centerless Virasoro algebra and the Heisenberg algebra.