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Article Dans Une Revue Journal of Noncommutative Geometry Année : 2018

Brackets in representation algebras of Hopf algebras

Résumé

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.

Dates et versions

hal-01189019 , version 1 (01-09-2015)

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Citer

Gwenael Massuyeau, Vladimir Turaev. Brackets in representation algebras of Hopf algebras. Journal of Noncommutative Geometry, 2018, 12 (2), pp.577-636. ⟨10.4171/JNCG/286⟩. ⟨hal-01189019⟩
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