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This follows a comment to split to a 2nd question Superalgebra and BRST supersymmetry 1: odd vs even
It is said that most of theories, the even elements of the superalgebra correspond to bosons and odd elements to fermions (but this is not always true; for example, the BRST supersymmetry is the other way around)..
More generally a gauge algebra (which is encoded into the BRST formulation of a gauge theory) form a super Lie algebroid, which in turn sometimes can be integrated to a super Lie groupoid.
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