Brackets in representation algebras of Hopf algebras

  • Gwénaël Massuyeau

    Université de Bourgogne, Dijon, France
  • Vladimir Turaev

    University of Indiana, Bloomington, USA

Abstract

For any graded bialgebras and , we define a commutative graded algebra representing the functor of -representations of . When is a cocommutative graded Hopf algebra and is a commutative ungraded Hopf algebra, we introduce a method deriving a Gerstenhaber bracket in from a Fox pairing in and a balanced biderivation in . 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.

Cite this article

Gwénaël Massuyeau, Vladimir Turaev, Brackets in representation algebras of Hopf algebras. J. Noncommut. Geom. 12 (2018), no. 2, pp. 577–636

DOI 10.4171/JNCG/286