A general construction method for graded Casimir elements and central extensions is given for color Lie algebras, with explicit examples for sl(2) graded by Z_3^2 and for q(n), osp(m|2n) graded by Z_2^2.
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Affine extensions of Z2^2-graded osp(1|2) yield a Z2^2-graded Virasoro algebra with non-trivially graded central element via Sugawara construction, supported by a developed theory of invariant bilinear forms on graded superalgebras.
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Graded Casimir elements and central extensions of color Lie algebras
A general construction method for graded Casimir elements and central extensions is given for color Lie algebras, with explicit examples for sl(2) graded by Z_3^2 and for q(n), osp(m|2n) graded by Z_2^2.
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Affine extensions of $\mathbb{Z}_2^2$-graded $osp(1|2)$ and Virasoro algebra
Affine extensions of Z2^2-graded osp(1|2) yield a Z2^2-graded Virasoro algebra with non-trivially graded central element via Sugawara construction, supported by a developed theory of invariant bilinear forms on graded superalgebras.