Classification of Z2-graded modules of intermediate series over a Block-type Lie algebra

Let L be the Lie algebra of Block type with basis {L-i,L- j vertical bar i, j is an element of Z} and relations [L-i,L- j, L-k,L- l] = (( j + 1) k - (l + 1)i) L-i vertical bar k,L- j vertical bar l. Since L is Z(2)-graded, it is natural to study Z(2)-graded modules over L. In this paper, Z(2)-graded L-modules of the intermediate series are classified.