Brackets in representation algebras of Hopf algebras
Brackets in representation algebras of Hopf algebras
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Hopf 代数的表示代数中的括号
DOI：
10.4171/jncg/286
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发表时间：
2015
影响因子：
0.9
通讯作者：
V. Turaev
中科院分区：
文献类型：
--
作者：
G. Massuyeau;V. Turaev
对任意分次双代数A和B，定义了一个交换分次代数A_B，它表示A的B-表示的函子.当$A$是一个余交换分次Hopf代数，$B$是一个交换未分次Hopf代数时，本文介绍了一种由$A$中的Fox对和$B$中的平衡双导子导出$A_B$中的Gerstenhaber括号的方法.我们的建设的灵感来自货车登伯格的非交换泊松几何，并可被视为一个代数推广的Atiyah-博特-戈德曼泊松结构的模空间的表示的表面群。
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.