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arXiv · 1104.4820

Infinite-dimensional Compact Quantum Semigroup

Marat A. Aukhadiev·Suren A. Grigoryan·Ekaterina V. Lipacheva
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Abstract

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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Marat A. Aukhadiev, Suren A. Grigoryan, Ekaterina V. Lipacheva. 2011-04-25. Infinite-dimensional Compact Quantum Semigroup. https://doi.org/10.1134/s199508021104007x

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