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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)..

  • Is BRST supersymmetry necessary and sufficient to be in the forms of Lie superalgebra? (Does BRST supersymmetry generate some Lie group manifolds if it has Lie superalgebra? Or can BRST supersymmetry generate exotics beyond?
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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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