BRST Cohomology is Lie Algebroid Cohomology

Understand

In this paper we demonstrate that the exterior algebra of an Atiyah Lie algebroid generalizes the familiar notions of the physicist's BRST complex.

• To reach this conclusion, we develop a general picture of Lie algebroid isomorphisms as commutative diagrams between algebroids preserving the geometric structure encoded in their brackets.
• We illustrate that a necessary and sufficient condition for such a diagram to define a morphism of Lie algebroid brackets is that the two algebroids possess gauge-equivalent connections.
• This observation indicates that the aforementioned set of Lie algebroid isomorphisms should be regarded as equivalent to the set of local diffeomorphisms and gauge transformations.