Affine extensions of ℤ22-graded osp(1|2) and Virasoro algebra

It is known that there are two inequivalent [Formula: see text]-graded [Formula: see text] Lie superalgebras. Their affine extensions are investigated and it is shown that one of them admits two central elements, one is non-graded and the other is [Formula: see text]-graded. The affine [Formula: see text]-[Formula: see text] algebras are used by the Sugawara construction to study possible [Formula: see text]-graded extensions of the Virasoro algebra. We obtain a [Formula: see text]-graded Virasoro algebra with a non-trivially graded central element. Throughout the investigation, invariant bilinear forms on [Formula: see text]-graded superalgebras play a crucial role, so a theory of invariant bilinear forms is also developed.