Infinite-dimensional紧量子半群
Infinite-dimensional Compact Quantum Semigroup
摘要：
本文在Toeplitz代数$\mathcal{T}$上构造了一个紧量子半群结构。证明了在对偶代数$\mathcal{T}^*$中存在一个子代数，该子代数同构于具有卷积积的圆上的正则Borel测度代数.证明了Haar泛函在对偶代数和上述子代数中的存在性。同时也证明了$\mathcal{T}$与弱霍普夫代数的结构之间的联系。
英文摘要：
In this paper we construct a compact quantum semigroup structure on the Toeplitz algebra $\mathcal{T}$. The existence of a subalgebra, isomorphic to the algebra of regular Borel's measures on a circle with convolution product, in the dual algebra $\mathcal{T}^*$ is shown. The existence of Haar functionals in the dual algebra and in the above-mentioned subalgebra is proved. Also we show the connection between $\mathcal{T}$ and the structure of weak Hopf algebra.
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