Geodesic
A compact quantum semialgebra generated by an isometry
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 89-93.

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In this paper we construct a compact quantum semigroup structure on a Toeplitz algebra. We prove the existence of a subalgebra in the dual algebra isomorphic to the algebra of regular Borel measures on a circle with the convolution product. We also prove the existence of a Haar functionals in the dual algebra and in the subalgebra mentioned above. We show that this compact quantum semigroup contains a dense subalgebra with the structure of a weak Hopf algebra.
Keywords: quantum semigroup, quantum group, Haar functional, Toeplitz algebra, weak Hopf algebra, inverse semigroup. 
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     author = {M. A. Aukhadiev and S. A. Grigoryan and E. V. Lipacheva},
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M. A. Aukhadiev; S. A. Grigoryan; E. V. Lipacheva. A compact quantum semialgebra generated by an isometry. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 89-93. http://geodesic.mathdoc.fr/item/IVM_2011_10_a9/

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