COMPLETELY POSITIVE MULTIPLIERS OF QUANTUM GROUPS
COMPLETELY POSITIVE MULTIPLIERS OF QUANTUM GROUPS
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DOI：
10.1142/s0129167x12501327
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发表时间：
2011-07
影响因子：
0.6
通讯作者：
Matthew Daws
中科院分区：
文献类型：
--
作者：
Matthew Daws
我们证明了算子代数量子群（无论是局部紧量子群，还是来自模或可管理的乘酉的量子群）的对偶的卷积代数的任何完全正乘子都可以通过g的酉共表示以规范的方式导出。由此可见，L1(g)的完全正乘子与泛量子群上的正泛函之间存在一个阶双射。我们提供了Junge、Neufang、阮的表示结果与乘数的表示元素之间的直接联系，并以此来表明它们的表示映射总是弱*-弱*-连续的。
We show that any completely positive multiplier of the convolution algebra of the dual of an operator algebraic quantum group 𝔾 (either a locally compact quantum group, or a quantum group coming from a modular or manageable multiplicative unitary) is induced in a canonical fashion by a unitary corepresentation of 𝔾. It follows that there is an order bijection between the completely positive multipliers of L1(𝔾) and the positive functionals on the universal quantum group . We provide a direct link between the Junge, Neufang, Ruan representation result and the representing element of a multiplier, and use this to show that their representation map is always weak*–weak*-continuous.