Categorical duality for Yetter-Drinfeld algebras
Categorical duality for Yetter-Drinfeld algebras
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DOI：
10.4171/dm/476
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发表时间：
2013-10
影响因子：
0.9
通讯作者：
S. Neshveyev;M. Yamashita
中科院分区：
文献类型：
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作者：
S. Neshveyev;M. Yamashita
研究了由紧量子群G在单位C * -代数上的作用所定义的(RepG)-模范畴上的张量结构。我们证明了有一个定义模结构的张量积相当于将G的作用丰富为编织交换的叶氏-德林菲尔德代数的结构。这证明了编织交换叶氏-德林菲尔德G- C * -代数的范畴等价于由RepG生成酉十量函子到C * -张量范畴的范畴。为了说明这种等价性，我们讨论了C(G)中商型的共理想、Hopf-Galois扩展和非交换泊松边界。
We study tensor structures on (RepG)-module cate- gories defined by actions of a compact quantum group G on unital C ∗ -algebras. We show that having a tensor product which defines the module structure is equivalent to enriching the action of G to the structure of a braided-commutative Yetter-Drinfeld algebra. This shows that the category of braided-commutative Yetter-Drinfeld G- C ∗ -algebras is equivalent to the category of generating unitary ten- sor functors from RepG into C ∗ -tensor categories. To illustrate this equivalence, we discuss coideals of quotient type in C(G), Hopf-Galois extensions and noncommutative Poisson boundaries.