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Lie superalgebra structures in H-center dot (g;g)
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| Organization: | University of Stockholm |
| Organization: | University of Stockholm |
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| Czechoslovak Journal of Physics |
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Abstract Let g=vect(M) be the Lie (super)algebra of vector fields on any connected (super)manifold M; let ldquo-rdquo be the change of parity functor, C i and H i the space of i-chains and i-cohomology. The Nijenhuis bracket makes into a Lie superalgebra that can be interpreted as the centralizer of the exterior differential considered as a vector field on the supermanifold associated with the de Rham bundle on M. A similar bracket introduces structures of DG Lie superalgebra in L * and for any Lie superalgebra g. We use a Mathematica-based package SuperLie (already proven useful in various problems) to explicitly describe the algebras l * for some simple finite dimensional Lie superalgebras g and their ldquorelativesrdquo - the nontrivial central extensions or derivation algebras of the considered simple ones.
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Lie superalgebras, cohomology
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http://www.equaonline.com/math/SuperLie/
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