Abstract
For any graded bialgebras A and B , we define a commutative graded algebra A_B representing the functor of B -representations of A . When A is a cocommutative graded Hopf algebra and B is a commutative ungraded Hopf algebra, we introduce a method deriving a Gerstenhaber bracket in A_B from a Fox pairing in A and a balanced biderivation in B . Our construction is inspired by Van den Bergh’s non-commutative Poisson geometry, and may be viewed as an algebraic generalization of the Atiyah–Bott–Goldman Poisson structures on moduli spaces of representations of surface groups.
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