Infinite-dimensional Compact Quantum Semigroup

Details Infinite-dimensional Compact Quantum Semigroup Infinite-dimensional Compact Quantum Semigroup

2011-04-25

arxiv.org/abs/1104.4820v1

Mathematics

Quantum Algebra

17 pages

Scientific paper

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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