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A description of Kac-systems of multiplicative unitary operators

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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 Ã( 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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  1. Department of Mathematics, Qufu Normal University, 273165, Qufu, China

    Xiaoxia Zhang

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  1. Xiaoxia Zhang
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Correspondence to Xiaoxia Zhang.

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Zhang, X. A description of Kac-systems of multiplicative unitary operators. Sci. China Ser. A-Math. 44, 1439–1445 (2001). https://doi.org/10.1007/BF02877073

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