Infinite-dimensional Compact Quantum Semigroup
Abstract
In this paper we construct a compact quantum semigroup structure on the Toeplitz algebra 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 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 T and the structure of weak Hopf algebra.
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