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 = | ||||
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. |