On ∞ - Lie Urs
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چکیده
We discuss actions of Lie n-groups and the corresponding action Lie n-groupoids; discuss actions of Lie n-algebras (L∞-algebras) and the corresponding action Lie n-algebroids; and discuss the relation between the two by integration and differentiation. As an example of interest, we discuss the BRST complex that appears in quantum field theory. We describe it as the Chevalley-Eilenberg algebra of the Lie n-algebroid which linearizes the action n-groupoid (the homotopy quotient) of a gauge n-group acting on the space of fields. This identifies the ghosts-of-ghosts of degree k as the cotangents to the space of k-morphisms of this action n-groupoid. Several separate aspects of what we say here are essentially " well known " to those who know it well. But a coherent description as attempted here is certainly missing in the literature and deserves to be better known.
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