nLab super Lie algebroid

Idea

The evident Lie algebroid-version of what is discussed at super L-∞ algebra.

Examples

• The super-dg-algebra which si the de Rham complex of superdifferential forms on a supermanifold is the Chevalley-Eilenberg algebra of the super-tangent Lie algebroid of that manifold. See the discussion at signs in supergeometry.

The BRST complex of a supersymmetric field theory (e.g FFK 89 for the superstring) is the Chevalley-Eilenberg algebra of the corresponding super-action Lie algebroid.

References

• José Figueroa-O'Farrill, Takashi Kimura, The BRST cohomology of the NSR string: vanishing and “-ghost’‘ theorems, Comm. Math. Phys.

  Volume 124, Number 1 (1989), 105-132. (Euclid)

• Alexander Belopolsky, De Rham Cohomology of the Supermanifolds and Superstring BRST Cohomology, Phys.Lett. B403 (1997) 47-50 (arXiv:hep-th/9609220)