Quantum symmetry groups of C*‐algebras equipped with orthogonal filtrations
Quantum symmetry groups of C*‐algebras equipped with orthogonal filtrations
复制标题
配备正交过滤的 C* 代数的量子对称群
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Adam G. Skalski
中科院分区：
文献类型：
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作者：
T. Banica;Adam G. Skalski
在Goswami关于非交换流形的量子等距群的研究的启发下，我们定义了具有正交滤波的单位C*‐代数a的量子对称群作为以滤波保持方式作用于a的紧量子群范畴中的普遍对象。证明了这种普遍对象的存在性，并讨论了几个例子。特别地，我们研究了作用于自由群对偶并同时保持字长和块长的通用量子群。
Motivated by the work of Goswami on quantum isometry groups of non‐commutative manifolds, we define the quantum symmetry group of a unital C*‐algebra A equipped with an orthogonal filtration as the universal object in the category of compact quantum groups acting on A in a filtration‐preserving fashion. The existence of such a universal object is proved and several examples discussed. In particular, we study the universal quantum group acting on the dual of the free group and preserving both the word length and the block length.