Brackets in representation algebras of Hopf algebras

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 group


Publication Date:
Jun 11 2018
Date Submitted:
Jun 28 2019
Citation:
Journal of Noncommutative Geometry
12
2
External Resources:




 Record created 2019-06-28, last modified 2019-08-06


Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)