Abstract
Let F be a field of characteristic p > 3, and L = ⊕i≥minus;1Li the finite-dimensional transitive Z-graded simple Lie superalgebral over F. In this paper L is determined if the Z-graded Lie superalgebra L−1 ⊕L0 is isomorphic to the L−1⊕pl (L−1) or L−1⊕spl (L−1).
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