Brackets in representation algebras of Hopf algebras

被引：1

作者：

Massuyeau, Gwenael ^{[1
,2
]}

Turaev, Vladimir ^{[3
]}

机构：

[1] Univ Bourgogne Franche Comte, IMB, F-21000 Dijon, France

[2] CNRS, F-21000 Dijon, France

[3] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

来源：

JOURNAL OF NONCOMMUTATIVE GEOMETRY | 2018年 / 12卷 / 02期

关键词：

Poisson algebra; Hopf algebra; representation algebra; Gerstenhaber algebra; quasi-Poisson algebra; double Poisson algebra; POISSON STRUCTURES; MODULI SPACES; SURFACES; MANIFOLDS;

D O I：

10.4171/JNCG/286

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：577 / 636

页数：60

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