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Lie superalgebra structures in H-center dot (g;g)

Pavel Grozman
Organization: University of Stockholm
Department: Mathematics
Dimitry Leites
Organization: University of Stockholm
Department: Mathematics
Journal / Anthology

Czechoslovak Journal of Physics
Year: 2004
Volume: 54
Issue: 11
Page range: 1313-1319

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.

*Mathematics > Algebra > Group Theory

Lie superalgebras, cohomology