An Algebraic Duality Theory for Multiplicative Unitaries
An Algebraic Duality Theory for Multiplicative Unitaries
复制标题
乘法酉的代数对偶理论
DOI：
10.1142/s0129167x01000770
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Universita' di RomaTor Vergata
中科院分区：
文献类型：
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作者：
S. Doplicher;C. Pinzari;J. E. R. D. D. Matematica;U. Sapienza'';Italy;D. .. Matematica;Universita' di RomaTor Vergata
乘法单位用一对相对深度为2的交换移位来描述。它们可以由张量C*-范畴中的双灵希尔伯特空间生成。Takesaki-Tatsuuma对偶定理的代数模拟抽象地刻画了由单位自同态作用的C*-代数，这些自同态与乘法酉正则表示有内在的联系。如果相应的乘法么正则作用在可分的Hilbert空间上，则相应的C*-代数是简单的且确实是可分的。范畴类比给出了乘法酉极小表示范畴的内部刻画。讨论了Cuntz代数的自同态，以及张量C~*-范畴中辫子对称的概念。
Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality Theorem characterizes abstractly C*-algebras acted on by unital endomorphisms that are intrinsically related to the regular representation of a multiplicative unitary. The relevant C*-algebras turn out to be simple and indeed separable if the corresponding multiplicative unitaries act on a separable Hilbert space. A categorical analogue provides internal characterizations of minimal representation categories of a multiplicative unitary. Endomorphisms of the Cuntz algebra related algebraically to the grading are discussed as is the notion of braided symmetry in a tensor C*-category.