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. 
@article{IVM_2011_10_a9,
     author = {M. A. Aukhadiev and S. A. Grigoryan and E. V. Lipacheva},
     title = {A compact quantum semialgebra generated by an isometry},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {89--93},
     publisher = {mathdoc},
     number = {10},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_10_a9/}
}
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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/