A description of Kac-systems of multiplicative unitary operators |
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Authors: | Xiaoxia Zhang |
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Affiliation: | Department of Mathematics, Qufu Normal University, Qufu 273165, China; Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100864, China |
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Abstract: | Let V be a multiplicative unitary operator on a separable Hilbert spaceH, then there are two subalgebras ofB( H) denoted byA( V) and ?( V), respectively, which correspond to V. If V satisfiesV 2 =I, then we will obtain the necessary and sufficient condition of Baaj and Skandalis’ main theorem, i.e.V has a Kac-system if and only if the linear closed space of the product of the above two algebras is the compact operator space; with this condition the above algebras are also quantum groups. |
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Keywords: | multiplicative unitary operators regular irreducible Kac-systems quantum groups |
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