Mathematics – Representation Theory
Scientific paper
2005-09-21
Czech. J. Phys. v. 54, 2004, no. 11, 1313--1319
Mathematics
Representation Theory
6 pages, LaTeX
Scientific paper
On a given manifold M, the Nijenhuis bracket makes the superspace of vector-valued differential forms 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 the superspaces of cochains and cohomology with coefficients in the adjoint module for any Lie superalgebra. We use a Mathematica--based package SuperLie (already proven useful in various problems) to explicitly describe these Lie superalgebras for some simple finite dimensional Lie superalgebras and their ``relatives'' (the nontrivial central extensions or derivation algebras of the considered simple ones).
Grozman Pavel
Leites Dimitry
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